This paper takes a novel approach to studying the existence and stability of Nash equilibria in N-firm Cournot–Bertrand oligopolies. First, we show that such games can be monotonically embedded into a game of strategic heterogeneity, so that each firm best responds to the choices of all other firms in a monotonic way. We then show that this monotonicity can be exploited to derive conditions which guarantee the existence of a unique, dominance solvable Nash equilibrium which is stable under all adaptive (...) dynamics. These conditions constitute a strict improvement over existing results in the literature. Finally, we examine the effect on these conditions resulting from additional firms entering the market. (shrink)

This paper shows that expected utility belongs to the intersection of models satisfying betweenness and a homotheticity condition for risky choice. Betweenness models can accommodate variable risk attitudes, originally highlighted by the Allais paradox, by restricting indifference curves to be linear while allowing non-parallelism. Homotheticity, in contrast, restricts indifference curves to be parallel while permitting non-linearities, such as those highlighted by inverse-S probability weighting. Data from an experiment indicate that approximately 2/3s of participants satisfied homotheticity. Of this group, about half (...) satisfied the expected utility hypothesis. The other half violated expected utility and therefore betweenness. These results indicate that homothetic preferences, and in particular those violating betweenness, can be empirically relevant for decision making under risk. (shrink)

This paper shows that temperance is the highest order risk preference condition for which spreading N independent and unfair risks provides the highest level of welfare than any other possible allocations of risks. These results are also interpreted through the concept of N-superadditivity of the utility premium. This paper provides a novel application of temperance, not in terms of two risks as it is common, but in terms of N risks.

The method of supergrading is introduced for deriving a ranking of items from scores or grades awarded by several people. Individual inputs may come in different languages of grades. Diversity in grading standards is an advantage, enabling rankings derived by this method to separate more items from one another. A framework is introduced for studying grading on the basis of observations. Measures of accuracy, reliability and discrimination are developed within this framework. Ability in grading is characterized for individuals and groups (...) as the capacity to grade reliably, accurately and at a high level of discrimination. It is shown that the collective ability of a supergrading group with diverse standards can be greater than that of a less diverse group whose members have greater ability. (shrink)

Zeckhauser’s paradox has puzzled and entertained many rationality enthusiasts for almost half a century. You are forced to play a Russian Roulette with a 6-chamber revolver containing either two bullets, or four bullets. Would you pay more to remove the two bullets in than you would to remove one in? Most would say yes, but rational considerations based on the classical utility theory suggest you should not. We discuss a possible solution within the classical framework, by explicitly stating and accounting (...) for more detailed preferences in terms of fewer bullets and smaller debt. To a large extent, the paradox arises due to a surreptitious trespassing of Savage’s Small-World utilities implied by a limited set of preferences to govern a larger world containing potentially conflicting preferences. To avoid logical issues associated with death in the roulette, we also describe a non-fatal game-show version, where you choose one box out of six that could be either empty or contain prize money. Here, the paradox arises when you pay from the prize money, but not when you pay from your own money. In summary, the paradox provides a useful lesson about the normative role of the utility function as a rational guide for our decisions and preferences. (shrink)

In light of the so-called ‘chaos theorems’ from social choice theory, William Riker argues that the indeterminacy of majority rule leads to voting cycles making democratic decisions arbitrary and meaningless. Moreover, when the core is empty, majority instability correlates with the level of conflict among actors. This study uses laboratory committee decision-making experiments to provide an empirical test of both aspects of Riker’s argument. Committees make repeated majority decisions over 20 periods picking points from a two-dimensional policy space. The experiment (...) manipulates committee members’ preferences and thus varies the existence of a core and the level of conflict between group members. The experimental results contradict Riker’s interpretation of the chaos theorems’ implications. Thus, the core exhibits less attraction than generally assumed. Moreover, an empty core is not associated with increased majority rule instability. Instead, conflicting preferences lead to more instability irrespective of the existence of an equilibrium. (shrink)

This paper analyzes the core of cooperative games generated by asymmetric aggregative normal-form games, i.e., games where the payoff of each player depends on his strategy and the sum of the strategies of all players. We assume that each coalition calculates its worth presuming that the outside players stand alone and select individually best strategies. We show that under some mild monotonicity assumptions on payoffs, the resulting cooperative game is balanced and has a non-empty core. Our paper thus offers an (...) existence result for a core notion which is frequently encountered in the theory and applications of cooperative games with externalities. (shrink)

The present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite Richter–Peleg multi-utility for a preorder are studied. It is well known that, given a preorder on a topological space, if there is a lower semicontinuous Richter–Peleg multi-utility, then the topology of the space must be finer than the Upper topology. However, this condition fails to be sufficient. Instead of search (...) for properties that must be satisfied by the preorder, we study finer topologies which are necessary or/and sufficient for the existence of semicontinuous representations. We prove that Scott topology must be contained in the topology of the space in case there exists a finite lower semicontinuous Richter–Peleg multi-utility. However, the existence of this representation cannot be guaranteed. A sufficient condition is given by means of Alexandroff’s topology, for that, we prove that more order implies less Alexandroff’s topology, as well as the converse. Finally, the paper is implemented with a topological study of the maximal elements. (shrink)

Often in insurance decision making, there are risk factors on which the insurer has an informational advantage over the consumer. But when the insurer sets and posts a premium for the consumer to consider, the consumer can potentially use the premium as an informational cue for the loss probability, and thereby to reduce the insurer’s informational advantage. We study, by means of a behavioral model, how consumers would use the premium as an informational cue in such contexts. The belief formation (...) process in our model assumes that both prior knowledge and the premium might have an impact on the consumer’s estimate of the loss probability. Moreover, the premium impacts the estimate through an anchoring-and-adjustment process. The model potentially leads to violations of rational expectations, with which the consumer overestimates the loss probability beyond what could be inferred from the premium, given the premise that the insurer must seek to break even or earn an expected profit. Our model analysis moreover implies that the frequency of such violations is non-increasing as the premium increases. Last, the model implies a generally inverted-U relationship between insurance demand and the premium so that the demand is upward sloping at low premium levels and downward sloping at high premium levels. A pilot field study and a laboratory experiment provide robust evidence for our model implications and calibrations for its parameters. (shrink)

Most laboratory experiments studying Tullock contest games find that bids significantly exceed the risk-neutral equilibrium predictions. We test the generalisability of these results by comparing a typical experimental implementation of a contest against the familiar institution of a ticket-based raffle. We find that in the raffle initial bid levels are significantly lower and bids adjust more rapidly towards expected-earnings best responses. We demonstrate the robustness of our results by replicating them across two continents at two university labs with contrasting student (...) profiles. (shrink)

Bradley develops some theory of the linear opinion pool, in apparent contradiction to results of Dawid et al.. We investigate the sources of these contradictions, and in particular identify a mathematical error in Bradley that invalidates his main result.

Several studies on time preference have found time inconsistency in both gain and loss preferences. However, the relationship between the two within the same person remains unclear; that is, does an individual who demonstrates time inconsistency for gain outcomes do so for losses as well? This paper reports on individuals’ time inconsistency for gains and losses in a laboratory setting. To obtain a precise comparison of individuals’ time inconsistency for gains and losses, we used Rohde’s “DI -index” :1700–1716, 2018) and (...) measured the level of time inconsistency, rather than merely identifying whether TI was present. This index represents how strongly a person exhibits present bias, and easily extends to the comparison between gain and loss preferences within the same person. Further, it allows the experiment to test for so-called future bias, which has been a focus area in recent time inconsistency literature. It is elicited through a non-parametric method, which avoids any specification errors in the analysis. Our findings are as follows: first, we found future bias in preferences for not only gains but also losses, and we confirmed that this tendency is consistent with previous findings on preferences for gains. Second, a positive correlation between time inconsistency for gains and losses was found at the individual level. Indeed, we could not find a significant difference between the two in most cases. (shrink)

Scoring rules constitute a particularly popular technique for aggregating a set of rankings. However, setting the weights associated with rank positions is a crucial task, as different instantiations of the weights can often lead to different winners. In this work we adopt minimax regret as a robust criterion for determining the winner in the presence of uncertainty over the weights. Focusing on two general settings we provide a characterization of the minimax regret rule in terms of cumulative ranks, allowing a (...) quick computation of the winner. We then analyze the properties of using minimax regret as a social choice function. Finally we provide some test cases of rank aggregation using the proposed method. (shrink)

Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure outcomes. The paper proposes (...) an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann :199–205, 1963, p. 201). (shrink)

While the philosophical literature has extensively studied how decisions relate to arguments, reasons and justifications, decision theory almost entirely ignores the latter notions. In this article, we elaborate a formal framework to introduce in decision theory the stance that decision-makers take towards arguments and counter-arguments. We start from a decision situation, where an individual requests decision support. We formally define, as a commendable basis for decision-aid, this individual’s deliberated judgment, a notion inspired by Rawls’ contributions to the philosophical literature, and (...) embodying the requirement that the decision-maker should carefully examine arguments and counter-arguments. We explain how models of deliberated judgment can be validated empirically. We then identify conditions upon which the existence of a valid model can be taken for granted, and analyze how these conditions can be relaxed. We then explore the significance of our framework for the practice of decision analysis. Our framework opens avenues for future research involving both philosophy and decision theory, as well as empirical implementations. (shrink)

Models of choice over menus aim at capturing the effect of some behavioral or non-standard element of decision-making on the behavior of a single decision-maker. These models are usually compared with the standard model of choice over menus, in which the decision-maker chooses a menu whose best item is better than that of all other available ones. However, in many empirical settings such as experimental studies, choice data come from a population of decision-makers with possibly heterogeneous attitudes and tastes. This (...) heterogeneity can make the observed choices over menus stochastic. This fact calls for a stochastic characterization of models of choice over menus to be able to better compare and contrast different models empirically. In this paper, I do this task for the standard model, which would be an extension of the random utility model to the realm of choice over menus. In particular, I provide the necessary and sufficient conditions, i.e., axioms on choice data over menus for it to be consistent with a population of decision-makers each of whom behaves according to the standard model. The axioms that characterize the model are the axiom of revealed stochastic preferences over singletons and three rationality axioms. (shrink)

It is well known that the Penrose–Banzhaf index of a weighted game can differ starkly from corresponding weights. Limit results are quite the opposite, i.e., under certain conditions the power distribution approaches the weight distribution. Here we provide parametric examples that give necessary conditions for the existence of limit results for the Penrose–Banzhaf index.

There are few models of price competition in a homogeneous-good market which permit general asymmetries of information amongst the sellers. This work studies a price game with discontinuous payoffs in which both costs and market demand are ex ante uncertain. The sellers evaluate uncertain profits with maximin expected utilities exhibiting ambiguity aversion. The buyers in the market are permitted to split between sellers tieing at the minimum price in arbitrary ways which may be deterministic or random. The role of the (...) primitives in determining equilibrium prices in the market is analyzed in detail. (shrink)

The main purpose of this paper is to compute the theoretical likelihood of some electoral outcomes under the impartial anonymous culture in four-candidate elections by using the last versions of software like LattE or Normaliz. By comparison with the three-candidate case, our results allow to analyze the impact of the number of candidates on the occurrence of these voting outcomes.

Local proper scoring rules provide convenient tools for measuring subjective probabilities. Savage, 783–801, 1971) has shown that the only local proper scoring rule for more than two exclusive events is the logarithmic family. We generalize Savage by relaxing the properness and the domain, and provide simpler proof.

Lying for a strategic advantage is to be expected in commercial interactions. But would this be more or less obvious when lying could come from either party and question mutually profitable exchange? To explore this, we modify the acquiring-a-company game by letting both, buyer and seller, be privately informed. Specifically, the value of the company for the buyer is known only by the seller; whereas, only the buyer is aware by which proportion the sellers evaluation is lower than that of (...) the buyer. Before bargaining, both parties can reveal what they know via cheap-talk numerical messages. Game theoretically, the pooling equilibrium may or may not allow for trade depending on the commonly known expected evaluation discrepancy. By mutually revealing what one knows, one could boost trade and efficiency. Although strategic misreporting prevails quite generally, it is higher for sellers throughout the experiment. Regarding gender, women misreport less, especially as sellers, and offer higher prices. (shrink)

We use a controlled laboratory experiment to study firm’s protection against potential technological damages. The probability of a catastrophic event is known, and the firm’s costly investment in safety reduces it. The firm can also buy an insurance with full or partial refund against the consequences of the catastrophic event, which ultimately reduces the variance of the firm’s investment-in-safety lottery. The firm makes these two choices simultaneously, after observing the insurance contract proposed by an insurer who chooses this contract within (...) a set of premium–deductible combinations. We parametrize the insurer–firm game such that a risk-neutral insurer maximizes his expected profit by offering an actuarially fair contract with full insurance; a risk-neutral firm is indifferent between investing in safety and accepting a fair insurance contract. We aim at understanding whether investment in safety and insurance are substitutes or complements in the firm’s risk management of catastrophic events. In line with our predictions, the experimental results suggest that they are substitutes rather than complements: the firm’s investment in safety measures is affected by the insurer’s proposed contract, the latter usually involving only partial insurance. (shrink)

Panel data from the German SOEP is used to test for risk vulnerability in the wider population. Two different survey responses are analysed: the response to the question about willingness-to-take risk in general and the chosen investment in a hypothetical lottery. A convenient indicator of background risk is the VDAX index, an established measure of volatility in the German stock market. This is used as an explanatory variable in conjunction with HDAX, the stock market index, which proxies wealth. The impacts (...) of these measures on risk attitude are identifiable by exploiting the time dimension of the panel and matching survey months with corresponding observations from these time-varying factors. Both of the survey responses allow us to test for decreasing absolute risk aversion ; in one case, we find strong evidence of DARA, while in the other, we do not. Both survey responses also allow us to test for RV, and in both cases we find strong evidence. In the case of the hypothetical lottery response, we are also able to estimate a “coefficient of risk vulnerability”. This is defined as the absolute amount by which absolute risk aversion rises in response to a doubling of background risk. We estimate CRV to be between 1.03 and 1.27. (shrink)

Canonical economic agents act so as to maximize a single, representative, utility function. However, there is accumulating evidence that heterogeneity in thought processes may be an important determinant of individual behavior. This paper investigates the implications of a vector-valued generalization of the Expected Utility paradigm, which permits agents either to deliberate as per Homo economics, or to act impulsively. This generalized decision theory is applied to explain the crowding-out effect, irrational educational investment decisions, persistent social inequalities, the pervasive influence of (...) non-cognitive ability on socio-economic outcomes, and the dynamic relationships between non-cognitive ability, cognitive ability, and behavioral biases. These results suggest that the generalized decision theory warrants further investigation. (shrink)

Utilities of health states are often estimated to support public decisions in health care. People’s preferences may be imprecise, for lack of actual trade-off experience. We show how to elicit the utilities accounting for imprecision, discover the main drivers of imprecision, and compare several approaches to modelling health state utility data in the fuzzy setting. We extended the time trade-off questionnaire, to elicit utilities of states defined in the EQ-5D-3L descriptive system in184 respondents. Our study demonstrates that respondents are capable (...) of assessing their own imprecision and rigorous mathematical modelling is possible. The imprecision is larger than as inferred from the standard TTO method and is larger than estimation error, even in our smallish sample. Non-trading in TTO often results from imprecision, rather than lexicographic preferences for longevity over quality. People are especially imprecise in assessing the impact of usual activities on utility; also, the internal inconsistency of a health state increases the imprecision. Fuzzy least squares method seems best suited to assign disutilities to individual dimensions, while separately modelling the location of utility and amount of imprecision seems best to produce value sets. If crisp parameters are estimated, accounting for imprecision changes the results little. (shrink)

We investigate experimentally the relationship between risk and incentives in a principal–agent setting. In contrast to the existing empirical literature that describes such relationship as ‘tenuous’ or inconclusive, we find a clear negative relationship—supporting the prediction of the standard theoretical model. Specifically, we find that principals reduce the size of the offered piece rates with an increase in risk and instead provide positive fixed wages. Furthermore, we find no relationship between the variance in the performance and the effort choice of (...) the agent, and a strong positive relationship between the effort choice of the agents and the offered piece rates as well as fixed wage, suggesting positive reciprocity. Finally, we find evidence of social projection by the principals regarding the agents’ degree of risk aversion. (shrink)

Increasingly, experimental economists, when eliciting risk preferences using a set of pairwise-choice problems, have given subjects a third choice, namely that of saying, for example, ‘I am not sure about my preference’ or ‘I am not sure what to choose’. The implications for subjects of choosing this third option vary across experiments depending upon the incentive structure. Some experiments provide no direct financial implications: what is ‘played out’ at the end of the experiment is not influenced by subjects choosing this (...) middle column. In other experiments, if the middle column has been checked, then the payoff is determined by a randomisation of A and B. I report on an experiment, which adopts this latter incentive mechanism, and ask the question as to why people might choose this option, that is “why do they prefer randomisation?” I explore four distinct stories and compare their goodness-of-fit in explaining the data. My results show that the two of the four have the most empirical support. I conclude with a discussion of whether my results have anything to say about preference imprecision. (shrink)