One prevalent type of slippery slope argument has the following form: (1) by doing some initial act now, we will bring it about that we subsequently do some more extreme version of this act, and (2) we should not bring it about that we do this further act, therefore (3) we should not do the initial act. Such arguments are frequently regarded as mistaken, often on the grounds that they rely on speculative or insufficiently strong empirical premises. In this article (...) I point out another location at which these arguments may go wrong: I argue that, in their standard form, the truth of their empirical premises constitutes evidence for the falsity of their normative premises. If we will, as predicted, do the further act in the future, this gives us at least a prima facie reason to believe that the performance of this further act would be good, and thus something we should try to bring about. I end by briefly assessing the dialectic implications of my argument. I delineate a subset of slippery slope arguments against which my objection may be decisive, consider how the proponents of such arguments may evade my objection by adding further premises, and examine the likely plausibility of these additional premises. (shrink)

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also from “residual” (...) consumption in the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (shrink)

This paper considers the simple two-person two-period case of distributive judgement, and argues (a) that sensible intertemporal distributive principle should consider both the distribution of people's life time well-being and the distribution of people's well-being at each period and (b) that, if (a) is correct, Egalitarianism is more acceptable than Prioritarianism since the latter must choose either one.

Several areas of welfare economics seek to evaluate states of affairs as a function of interpersonally comparable individual utilities. The aim is to map each state of affairs onto a vector of individual utilities, and then to produce an ordering of these vectors that can be represented by a mathematical function assigning a real number to each. When this approach is used in intertemporal contexts, a central theoretical question concerns the evaluative weight to be applied to utility coming at (...) different times. This question concerns the rate of pure time preference, which is one key determinant of the social discount rate. This article argues that the standard philosophical account of pure time preference is mistaken, because it ascribes to economists a methodological commitment they need not, and often do not, accept. This in turn undercuts the most common philosophical objection to pure time preference, which traces at least to Rawls’s A Theory of Justice. The article then evaluates three further objections to pure time preference, concluding that it might still be defensible under certain circumstances. The article closes by articulating a final argument that is suggested by the “Social, Economic and Ethical Concepts and Methods” chapter of the most recent Intergovernmental Panel on Climate Change report. If this further argument is sound, it would constitute a decisive objection to pure time preference as it currently figures in much intertemporal welfare economics. (shrink)

Traumatic brain injuries to the frontal lobes are associated with many maladaptive forms of behavior. We investigated the association between brain damage and impulsivity, as measured by the rate of delay discounting. The main aim of this study was to test the hypothesis of steeper discounting of different amounts in a group of patients with frontal lobe damage. We used a delay discounting task in the form of a structured interview. A total of 117 participants were divided into five groups: (...) three neurological groups and two groups without brain damage. Our analyses showed that patients with focal damage to the frontal lobes demonstrated steeper delay discounting than other participants. Other clinical groups demonstrated similar discounting rates. The data pattern related to the magnitude effect on the group level suggested that the magnitude effect is absent in the group of patients with damage to the frontal lobes; however, results were less consistent on an individual level. Amount-dependent discounting was observed in only two groups, the healthy control group and the neurological group with other cortical areas damaged. (shrink)

Lewis ascribes the stubborn persistence of addictions to habit, itself a normal process that does not imply lack of responsiveness to motivation. However, he suggests that more dynamic processes may be involved, for instance that “our recurrently focused brains inevitably self-organize.” Given hyperbolic delay discounting, a reward-seeking internal marketplace model describes two processes, also normal in themselves, that may give rise to the “deep attachment” to addictive activities that he describes: People learn to interpret current choices as test cases for (...) how they can expect to choose in the future, thus recruiting additional incentive against a universal tendency to temporarily prefer smaller, sooner to larger, later rewards. However, when this incentive is not enough, the same interpretation creates incentive to abandon the failed area, leading to the abstinence violation effect and a localized weak will. Normal human value does not come entirely, or even mainly, from expectation of external rewards, but is generated endogenously in imagination. Hyperbolic discounting provides an account of how we learn to cultivate the hedonic importance of occasions for endogenous reward by building appetite. In this account, expectations of the far future have to be rewarded endogenously if they are be as important as currently rewarded alternatives; and this importance is prone to collapse. Both will and hedonic importance are recursive and thus hard to study by controlled experiment, but do represent modelable, reward-based hypotheses about the dynamic nature of habit. (shrink)

While broadly in agreement with the conclusion that the exponentially discounted utility model (EDU) is not a universally valid rationality standard, I want to defend some intertemporal rationality criteria related to EDU, which Craig Callender might not share. My commentary explores the tension between these intuitions and Callender's arguments. In the first place, I show that many of the concerns that he raises are in fact compatible with intertemporal consistency (and sometimes even with EDU). Secondly, I rebut those (...) arguments that directly challenge consistency. I conclude that while we disagree on the rationality of consistency, we can nevertheless agree on its non-universality and its limited justification of policy interventions. (shrink)

To the extent that acting fairly is in an individual's long-term interest, short-term impulses to cheat present a self-control problem. The only effective solution is to interpret the problem as a variant of repeated prisoner's dilemma, with each choice as a test case predicting future choices. Moral choice appears to be the product of a contract because it comes from self-enforcing intertemporal cooperation.

Intertemporal choice involves deciding between smaller, sooner and larger, later rewards. People tend to prefer smaller rewards that are available earlier to larger rewards available later, a phenomenon referred to as temporal or delay discounting. Despite its ubiquity in human and non-human animals, temporal discounting is subject to considerable individual differences. Here, we provide a critical narrative review of this literature and make suggestions for future work. We conclude that temporal discounting is associated with key socio-economic and health-related variables. (...) Regarding personality, large-scale studies have found steeper temporal discounting to be associated with higher levels of self-reported impulsivity and extraversion; however, effect sizes are small. Temporal discounting correlates negatively with future-oriented cognitive styles and inhibitory control, again with small effect sizes. There are consistent associations between steeper temporal discounting and lower intelligence, with effect sizes exceeding those of personality or cognitive variables, although socio-demographic moderator variables may play a role. Neuroimaging evidence of brain structural and functional correlates is not yet consistent, neither with regard to areas nor directions of effects. Finally, following early candidate gene studies, recent Genome Wide Association Study (GWAS) approaches have revealed the molecular genetic architecture of temporal discounting to be more complex than initially thought. Overall, the study of individual differences in temporal discounting is a maturing field that has produced some replicable findings. Effect sizes are small-to-medium, necessitating future hypothesis-driven work that prioritizes large samples with adequate power calculations. More research is also needed regarding the neural origins of individual differences in temporal discounting as well as the mediating neural mechanisms of associations of temporal discounting with personality and cognitive variables. (shrink)

It is commonly accepted that what we ought to do collectively does not imply anything about what each of us ought to do individually. According to this line of reasoning, if cooperating will make no difference to an outcome, then you are not morally required to do it. And if cooperating will be personally costly to you as well, this is an even stronger reason to not do it. However, this reasoning results in a self-defeating, yet entirely predictable outcome. If (...) everyone is rational, no one will cooperate, resulting in an aggregate outcome that is devastating for everyone. This dismal analysis explains why climate change and other collective action problems are so difficult to ameliorate. The goal of this paper is to provide a different, exploratory framework for thinking about individual reasons for action in collective action problems. I argue that the concept of commitment gives us a new perspective on collective action problems. Once we take the structure of commitment into account, this activates requirements of diachronic rationality that give individuals instrumental reasons to cooperate in collective action problems. (shrink)

People often feel that a period of time becomes longer when it is described in more detail or cut into more segments, which is known as the time unpacking effect. The current study aims to unveil how time unpacking manipulation impacts intertemporal decision making and whether the gain-loss valence of choices moderates such impacts. We recruited 87 college students and randomly assigned them to the experimental conditions to complete a series of intertemporal choice tasks. The subjective values of (...) the delayed choices were calculated for each participant and then analyzed. The results showed that participants perceived longer time delays and higher subjective values on the delayed gains in the time unpacking conditions than in the time packing conditions. These results suggest that time unpacking manipulation not only impacts time perception but also other factors, which in turn, influence the valuation of delayed outcomes and thereby intertemporal choices. The results are discussed in comparison to previous studies to highlight the complexity of the mechanism underlying the effect of time unpacking on intertemporal decision making. (shrink)

The disagreement about intertemporal coordination between Austrians and Keynesians is explained pointing out to differences both in the way expectations and motivations are treated and the methodological principles assumed by each view. Austrians believe that research should proceed showing first what guarantees a successful coordination in individualsŠ plans, and only latter showing which could hinder the “natural” course. Keynes, on the contrary, do not start with any ideal state of affairs, but allows economies to work either “good” or “bad” (...) according to the prevailing expectations among entrepreneurs. In this way uncertainty and expectations are fully incorporated into economic theory. A link between Austrian approach and popperian situational analysis is suggested. (shrink)

This paper proposes a novel account of why intertemporal decisions tend to display impatience: People pay more attention to the opportunity costs of choosing larger, later rewards than to the opportunity costs of choosing smaller, sooner ones. Eight studies show that when the opportunity costs of choosing smaller, sooner rewards are subtly highlighted, people become more patient, whereas highlighting the opportunity costs of choosing larger, later rewards has no effect. This pattern is robust to variations in the choice task, (...) to the participant population, and is observed for both incentivized and hypothetical choices. We argue that people are naturally aware of the opportunity costs associated with delayed rewards, but pay less attention to those associated with taking smaller, sooner ones. We conclude by discussing implications for theory and policy. (shrink)

This paper reports the results of a series of experiments examining intertemporal choice. The paper makes three contributions: First, it presents a new analytic device, the intertemporal choice triangle, which is analogous to the Marschak--Machina choice triangle used in the analysis of choice under risk. Second, we have developed a new experimental design based on the intertemporal choice triangle which allows subjects greater flexibility in making choices, and which allows the researcher to make more subtle inferences, than (...) are possible with designs previously employed. Subjects are able to create their most-preferred outcome in each choice situation by choosing a constrained linear combination of two extreme options. Third, our results show that while subjects do not typically maximize present value, they are significantly influenced break by present value considerations. We refer to this finding as it present value-seeking behavior. We find only weak evidence of several previously documented intertemporal choice anomalies in our framework. (shrink)

According to Chen's Linguistic Savings Hypothesis, our native language affects our economic behavior. We present three studies investigating how cross-linguistic differences in the grammaticalization of future-time reference affect intertemporal choices. In a series of decision scenarios about finance and health issues, we let speakers of altogether five languages that represent FTR with increasing strength, that is, Chinese, German, Danish, Spanish, and English, choose between hypothetical sooner-smaller and later-larger reward options. While the LSH predicts a present-bias that increases with FTR-strength, (...) our decision makers preferred later-larger options and this future-bias increased with FTR-strength. In multiple regressions, the FTR-strength effect persisted when controlled for socioeconomic and cultural differences. We discuss why our findings deviate from the LSH and ask in how far the FTR-strength effect represents a habitual constitution of linguistic relativity or an instance of online decision framing. (shrink)

A climate that is too cold to grow crops for part of the year demands foresight and self-control skills. To the extent that a culture has developed intertemporal bargaining, its members will have more autonomy, but pay the cost of being more compulsive, than members of societies that have not. Monetary resources will be a consequence but will also be fed back as a cause.

Typical justifications of prudence are based on the fact that we are temporally extended agents who remain numerically identical over time. After showing that prudential considerations should instead be based on our identity at a particular time, I outline a normative context for prudential reasons, based on a present commitment to temporal neutrality. I then consider how contingency in the content of a present commitment to temporal neutrality provides a flexible context that can help to resolve current debates about whether (...) agents are required to maximize value, maximin value, minimax loss or are required to conform to any of a host of other options on how to adjudicate various types of conflict between present and future values. (shrink)

The life-cycle theory of saving behavior (Modigliani, 1988) suggests that humans strive towards an equal intertemporal distribution of wealth. However, behavioral life-cycle theory (Shefrin & Thaler, 1988) proposes that people use self-control heuristics to postpone wealth until later in life. According to this theory, people use a system of cognitive budgeting known as mental accounting. In the present study it was found that mental accounts were used differently depending on if the income change was positive or negative. This was (...) shown both in a representative nationwide sample of households and in a student sample. Respondents were more willing to cut down on their propensity to consume when faced with an income decrease than to raise it when the income increased. Furthermore, contrary to the predictions of behavioral life-cycle theory, it was found that the respondents adjusted their propensity to consume the most when the income increases or decreases took place immediately. Hence, it is suggested that theories of intertemporal choice (e.g., Loewenstein, 1988; Loewenstein & Prelec, 1992) provide a better account of the data than does the behavioral lifecycle theory. (shrink)

Models of intertemporal choice draw on three evaluation rules, which we compare in the restricted domain of choices between smaller sooner and larger later monetary outcomes. The hyperbolic discounting model proposes an alternative-based rule, in which options are evaluated separately. The interval discounting model proposes a hybrid rule, in which the outcomes are evaluated separately, but the delays to those outcomes are evaluated in comparison with one another. The tradeoff model proposes an attribute-based rule, in which both outcomes and (...) delays are evaluated in comparison with one another: People consider both the intervals between the outcomes and the compensations received or paid over those intervals. We compare highly general parametric functional forms of these models by means of a Bayesian analysis, a method of analysis not previously used in intertemporal choice. We find that the hyperbolic discounting model is outperformed by the interval discounting model, which, in turn, is outperformed by the tradeoff model. Our cognitive modeling is among the first to offer quantitative evidence against the conventional view that people make intertemporal choices by discounting the value of future outcomes, and in favor of the view that they directly compare options along the time and outcome attributes. (shrink)

Intertemporal choice requires one to decide between smaller sooner and larger later payoffs and is captured by discount rates. Across two preregistered experiments testing three language pairs (Polish vs. English, Spanish, and German; Experiment 1) and with incentivized participants (Experiment 2), we found no evidence that using a foreign language decreased the strength or increased the consistency of intertemporal choices. On the contrary, there was some evidence of stronger discounting when a foreign language was used. We confirmed prior (...) findings that more reflective individuals discount less strongly but observed that they were just as (un)affected by using foreign language as less reflective individuals. Thus, we provide preliminary evidence that the foreign language effect is robust to individual differences in cognitive reflection. (shrink)

Intertemporal choice requires one to decide between smaller sooner and larger later payoffs and is captured by discount rates. Across two preregistered experiments testing three language pairs (Polish vs. English, Spanish, and German; Experiment 1) and with incentivized participants (Experiment 2), we found no evidence that using a foreign language decreased the strength or increased the consistency of intertemporal choices. On the contrary, there was some evidence of stronger discounting when a foreign language was used. We confirmed prior (...) findings that more reflective individuals discount less strongly but observed that they were just as (un)affected by using foreign language as less reflective individuals. Thus, we provide preliminary evidence that the foreign language effect is robust to individual differences in cognitive reflection. (shrink)

We consider a situation where an individual is facing an uncertain situation, but may costly alter his knowledge of the uncertainties. We study in this context how risk aversion may modify the individual search behavior. We consider a one-armed bandit problem (where one arm is safe and the other is risky) and study how the agent risk aversion can change the sequence of arms selected. The main result is that when the utility function is more concave, the agent has more (...) chances to select the safe arm. We also discuss how search is affected by risk aversion. (shrink)

We consider a situation where an individual is facing an uncertain situation, but may costly alter his knowledge of the uncertainties. We study in this context how risk aversion may modify the individual search behavior. We consider a one-armed bandit problem (where one arm is safe and the other is risky) and study how the agent risk aversion can change the sequence of arms selected. The main result is that when the utility function is more concave, the agent has more (...) chances to select the safe arm. We also discuss how search is affected by risk aversion. (shrink)

Recent ethical breeches by corporate governorsat the highest levels have called into questionwhether ethical attitudes have changed sincethe Corporate Raider scandals of the mid-1980s. We exploit a unique opportunity to follow-up ona previous investigation of college students inthe mid-1980s to analyze this question. Usinga similar survey instrument, we find thatstudents surveyed in 2001 are significantlyless accepting of the ethically questionablesituations in seven of 15 scenarios and moreaccepting in only one. Seven scenarios showedno significant change. We conclude that,overall, ethical attitudes of (...) students in 2001appear to have become higher over time. To theextent that current students are futurebusiness leaders, we find these results to beencouraging for the long term. (shrink)

The ability to delay rewards is one of the most useful qualities one may wish to develop. People who possess this quality achieve more successful careers, display better interpersonal skills and are less vulnerable to psychopathology, obesity or addictions. In the present online studies, we investigated the extent to which delay-of-reward behaviors in female participants can be improved by observing others mastering it. We developed an intertemporal choice (IC) paradigm in which participants had to make fictitious choices between sooner (...) smaller rewards and later bigger ones (e.g. $150 in one week vs $170 in 4 weeks). In Study 1 (N = 186), we found that participants who delayed more had higher socioeconomic statuses and were less likely to procrastinate, smoke or develop obesity. In Study 2 (N = 178), we exposed female participants to a role model who, faced with intertemporal choices, chose most of the time the delayed option. Results showed that, although participants were only asked to memorize the model’s decisions, they tended to choose the delayed option more often after than before exposure to the model. In Study 3 (N = 148), we found that the direction of the influence depended on the model’s behavior: Our female participants delayed more after having seen a high delay than a low delay model. In Study 4 (N = 370), we confirmed the effect of modeling on intertemporal choices in comparison to a control condition and showed that this effect was still significant three months after exposure to the model. Altogether, these results speak in favor of a high efficacy of modeling to develop self-control in women. (shrink)

An interesting phenomenon called “hidden opportunity cost of time effect” was detected in intertemporal choices. The majority of our participants preferred the smaller but sooner (SS) option to the larger but later (LL) option if opportunity cost was explicit. However, a higher proportion of participants preferred the LL to SS option if opportunity cost was hidden. This shift violates the invariance principle and opens a new way to encourage future-oriented behavior. By simply mentioning the ‘obvious’ opportunity cost of alternatives, (...) decision makers can be more informed in prioritizing their long-term goals rather than short-term goals. (shrink)

We conducted an intertemporal online experiment to examine the contagion of others’ positive and negative donation behaviors. We collected two sets of data during and after the peak of the COVID-19 pandemic in China. The participants donated to the charitable fund, “Against COVID-19, The China Charity Federation Is on the Move.” We further investigated the mediating effect of social anxiety on the link between the contagion of donation behaviors and the changes in the COVID-19 situation. A total of 1022 (...) participants participated in the intertemporal online experiment and were considered in the statistical analyses. Our findings were as follows. First, the donation behaviors of others significantly changed these participants’ initial donation decisions, with increased or decreased donation amounts being associated with a positive or negative donation behavior, respectively. Others’ positive donation behavior was more likely to nudge these participants into changing their initial decisions than negative donation behavior during the peak of the pandemic. However, such difference disappeared after the peak because the contagion of positive donation behavior significantly decreased along with the abatement of the pandemic. Second, the participants’ social anxiety decreased along with the abatement of the pandemic, and social anxiety completely mediated the relationship between the pandemic abatement and the decrease in the contagion of positive donation behaviors. These findings advance our understanding of the motivations and influence mechanism of individuals’ donation decisions in the current pandemic situation and help make informed policy making decisions. (shrink)

We agree with Ainslie's general approach to intertemporal choices and self-control. However, we argue that a concept of “will” is superfluous in explaining tradeoffs between SS (smaller and sooner) and LL (larger and later) rewards in a framework of temporal goal setting and goal aggregation. We provide an alternative framework of reference point-dependent tradeoffs between SS and LL options.

The purpose of this study is to explore the influence of consumers’ choice deferral behavior on their intertemporal choice preference. The empirical study shows that consumers’ choice deferral behavior can significantly affect their intertemporal decision preference through the level of hopefulness. Compared with non-choice deferral behavior, choice deferral behavior can improve the level of consumers’ sense of hopefulness, which then makes them prefer larger-longer interests in intertemporal decision-making. The effect of consumers’ sense of hopefulness on their (...) class='Hi'>intertemporal choice preference is moderated by their perceived information integrity. When the perceived information integrity is low, the effect of hopefulness on intertemporal decision preference will be enhanced, but when the perceived information integrity is high, the effect of hopefulness on intertemporal decision preference will not be affected. In addition, the theoretical and practical significance of this study and the prospect of future research are also discussed. (shrink)

Two experiments with undergraduates as subjects were carried out with the aim of replicating and extending previous results showing that the implication of the behavioral life-cycle hypothesis (H. M. Shefrin & R. H. Thaler, 1988) that people classify assets in different mental accounts (current income, current assets, and future income) may explain how consumption choices are influenced by temporary income changes. In both experiments subjects made fictitious choices between paying for a good in cash or according to a more expensive (...) installment plan after they had received an income which was either less, the same, or larger than usual. In Experiment 1 subjects were supposed to have savings so that the total assets were equal, whereas in Experiment 2 the total assets varied. The results of both experiments supported the role of mental accounts in demonstrating that subjects were unwilling to pay in cash after an income decrease even though they had access to saved money. Thus, in effect they chose to pay more for the good than they had to. Indicating a need for further refinement of the concept of mental account, choices to pay in cash after an income decrease tended to be more frequent when the consumption and savings motives were compatible than when they were incompatible. Furthermore, increasing the total assets made subjects more willing to pay in cash after an income decrease. (shrink)

This study formulates a two-factor empirical model under the intertemporal CAPM framework to evaluate the cross-sectional implications of socially responsible investments in the US equity market. Our results show that socially responsible investments have no asset pricing impact on the US market. We argue that this ‘no financial impact’ finding indicates that investors will not be disadvantaged financially by investing in socially responsible funds or corporations.

Despite various studies examining intertemporal choice with hypothetical rewards due to problematic real reward delivery, there remains no substantial evidence on the effect of the incentives on the decision confidence and cognitive process in intertemporal choice and no comprehensive exploration on the loss domain. Hence, this study conducts an eye-tracking experiment to examine the effect of incentive approach and measure participants' decision confidence using a between-subject design in both gain and loss domains. Results replicated previous findings which show (...) incentives do not affect intertemporal choice in the gain domain. In contrast, in the loss domain, participants in the incentivized group were more likely to choose the larger-later options than those in the non-incentivized group. Furthermore, the decision confidence and the mean fixation duration differed between the incentivized and non-incentivized groups in both gain and loss domains. These findings allow for a better understanding of the effect of incentives on intertemporal choice and provide valuable information for the design of incentives in future intertemporal experiments. (shrink)

People make different choices depending on which decision is the default option. In intertemporal choices, the default option is typically imposed externally. For example, people expect more for delaying the gain than are willing to pay for accelerating the future gain over the same period. We claim that apart from the external default, people’s choices are also influenced by the internal default such as the time perspective resulting in the reference point in the present. By manipulating the congruency between (...) the internal and external defaults, we show that incongruence between defaults decreases the strength of discounting of gains, but not of losses. (shrink)

Introduction George Loewenstein, Daniel Read, and Roy F. Baumeister P _L sychology and economics have a classic love-hate relationship. ...

Turn taking is observed in many field and laboratory settings captured by various widely studied 2 × 2 games. This article develops a repeated game model that allows us to systematically investigate turn-taking behavior in many 2 × 2 games, including the battle of the sexes, the game of chicken, the game of common-pool-resources assignment, and a particular version of the prisoners’ dilemma. We consider the “turn taking with independent randomizations” (TTIR) strategy that achieves three objectives: (a) helping the players (...) reach the turn-taking path, (b) resolving the question of who takes the good turn first, and (c) deterring defection. We determine conditions under which there exists a unique TTIR strategy profile that can be supported as a subgame-perfect equilibrium. We also show that there exist conditions under which an increase in the “degree of conflict” of the stage game leads to a decrease in the expected number of periods in reaching the turn-taking path. (shrink)