In this article, I analyze the circumstances of justice, that is, the background conditions that are necessary and sufficient for justice to exist between individual parties in society. Contemporary political philosophers almost unanimously accept an account of these circumstances attributed to David Hume. I argue that the conditions of this standard account are neither sufficient nor necessary conditions for justice. In particular, I contend that both a Hobbesian state of nature and a prisoner’s dilemma are cases in which the conditions (...) of the standard account obtain and yet no justice exists between parties. I propose an alternative set of generic circumstances of justice motivated by examples from game theory. Parties are in these generic circumstances with respect to each other when: (1) they are engaged in a conflictual coordination game with multiple strict Nash equilibrium points where, at any of these equilibria, some parties do not receive their greatest payoffs, and (2) they have common knowledge that each party is rational and follows her end of a strict equilibrium where no party receives her greatest payoff. These two conditions reflect the idea that justice requires all parties to make some sacrifices so that others can have more of the goods they need and want. I argue that these generic circumstances are necessary and sufficient conditions for parties to follow generic norms of justice, that is, mutually beneficial practices that require some sacrifices. Key Words: common knowledge • conflictual coordination • correlated equilibrium • moderate selfishness • moderate variable scarcity • rough equality. (shrink)

I resolve a previously unnoticed anomaly in the analysis of collective action problems. Some political theorists apply game theory to analyze the paradox of anarchy: War is apparently inevitable in anarchy even though all warring parties prefer peace over war. Others apply tipping threshold analysis to resolve the paradox of revolution: Joining a revolution is apparently always irrational even when an overwhelming majority of the population wish to replace their regime. The usual game theoretic analysis of anarchy yields the conclusion (...) that the suboptimal equilibrium of war is inevitable. The usual tipping threshold analysis of revolution yields the conclusion that the optimal equilibrium of successful revolution is possible. Yet structurally the collective action problems of anarchy and potential revolution are much the same. This suggests that tipping threshold analysis and game theory are incompatible methodologies, despite their widespread use in the social sciences. I argue that there is no real tension between game theory and tipping threshold analysis, even though these methodologies have developed largely independently of each other. I propose a Variable Belief Threshold model of collective action that combines elements of game theory and tipping threshold analysis. I show by example that one can use this kind of hybrid model to give compatible explanations of conflict in anarchy and successful revolution.1. Introduction2. Two Classic Problems, and Two Popular Analyses2.1. The paradox of anarchy2.2. The paradox of revolution3. Restating the Puzzle4. Evaluating the Prisoners’ Dilemma and S-Curve Models5. The Variable Belief Threshold ModelExample 5.1. A population of moderates with independent deviationsExample 5.2 A heterogeneous population with independent deviationsExample 5.3 A heterogeneous population with coordinated deviations6. ConclusionAppendix: Computer Simulations. (shrink)

Axelrod (The evolution of cooperation, 1984) and others explain how cooperation can emerge in repeated 2-person prisoner’s dilemmas. But in public good games with anonymous contributions, we expect a breakdown of cooperation because direct reciprocity fails. However, if agents are situated in a social network determining which agents interact, and if they can influence the network, then cooperation can be a viable strategy. Social networks are modelled as graphs. Agents play public good games with their neighbours. After each game, they (...) can terminate connections to others, and new connections are created. Cooperative agents do well because they manage to cluster with cooperators and avoid defectors. Computer simulations demonstrate that group formation and exclusion are powerful mechanisms to promote cooperation in dilemma situations. This explains why social dilemmas can often be solved if agents can choose with whom they interact. (shrink)

According to Hobbes, individuals care about their relative standing in a way that shapes their social interactions. To model this aspect of Hobbesian psychology, this paper supposes that agents have social preferences, that is, preferences about their comparative resource holdings. Introducing uncertainty regarding the social preferences of others unleashes a process of trust-unravelling, ultimately leading to Hobbes’s ‘state of war’. This Trust-unravelling Model incorporates important features of Hobbes’s argument that past models ignore.

This paper considers contractarianism as a method of justification. The analysis accepts the key tenets of contractarianism: expected utility maximization, unanimity as the criteria of acceptance, and social-scientific uncertainty of modelled agents. In addition to these three features, however, the analysis introduces a fourth feature: a criteria of rational belief formation, viz. Bayesian belief updating. Using a formal model, this paper identifies a decisive objection to contractarian justification. Insofar as contractarian projects approximate the Agreement Model, therefore, they fail to justify (...) their conclusions. Insofar as they fail to approximate the Agreement Model, they must explain which modelling assumption they reject. (shrink)

In this article, I argue that if one closely follows Hobbes' line of reasoning in Leviathan, in particular his distinction between the second and the third law of nature, and the logic of his contractarian theory, then Hobbes' state of nature is best translated into the language of game theory by an assurance game, and not by a one-shot or iterated prisoner's dilemma game, nor by an assurance dilemma game. Further, I support Hobbes' conclusion that the sovereign must always punish (...) the Foole, and even exclude her from the cooperative framework or take her life, if she defects once society is established, which is best expressed in the language of game theory by a grim strategy. That is, compared to existing game-theoretic interpretations of Hobbes, I argue that the sovereign plays a grim strategy with the citizens once society is established, and not the individuals with one another in the state of nature. (shrink)

Conventionalism as a distinct approach to the social contract received significant attention in the game-theoretic literature on social contract theory. Peter Vanderschraaf’s sophisticated and innovative theory of conventional justice represents the most recent contribution to this tradition and, in many ways, can be viewed as a culmination of this tradition. In this article, I focus primarily on Vanderschraaf’s defense of the egalitarian bargaining solution as a principle of justice. I argue that one particular formal feature of this bargaining solution, the (...) baseline consistency requirement, may stand in tension with other features of conventionalism as an approach to the social contract and limit the scope of Vanderschraaf’s theory to societies in which de facto an egalitarian sense of justice evolves. It limits the scope of Vanderschraaf’s theory in the face of moral diversity. A similar limitation applies to Vanderschraaf’s theory of democratic political authority. Despite these minor limitations, Vanderschraaf’s theory can only be seen as a major success and significant contribution to social contract theory. (shrink)

Game theory has proven useful in clarifying Hobbes’s argument that the state of nature will inevitably devolve into a state of war. Mathematically-leaning philosophers, however, have paid little attention to Rousseau’s depiction of the state of nature as a peaceful, asocial state of solitary wanderers. This paper articulates Rousseau’s critique of Hobbes in formal terms, which pinpoints two crucial issues in Hobbes’s account: the lack of an exit option and an unrealistic depiction of human nature. Building upon recent game-theoretic treatments (...) of Hobbes, we first construct a model that incorporates Rousseau’s criticisms by permitting an exit option and endogenizing human preferences and capacities. Second, we draw out the implications of Rousseau’s analysis for the question of political authority, which cannot be answered, as Hobbes believed, by invoking a hypothetical state of nature. (shrink)

Hobbes’s state of nature is often analyzed in two-person two-action non-cooperative games. By definition, this literature only focuses on duels. Yet, if we consider general games, i.e., with more than two agents, analyzing Hobbes’s state of nature in terms of duel is not completely satisfactory, since it is a very specific interpretation of the war of all against all. Therefore, we propose a definition of the state of nature for games with an arbitrary number of players. We show that this (...) definition coincides with the strategy profile considered as the state of nature in two-person games. Furthermore, we study what we call rational states of nature. We show that in rational states of nature, the utility level of any agent is equal to his maximin payoff. We also show that rational states of nature always exist in inessential games. Finally, we prove the existence of states of nature in a class of symmetric games. (shrink)

John Rawls’s most mature notion of political order is “stability for the right reasons.” Stability for the right reasons is the kind of political order that Rawls hoped a well-ordered society could ideally achieve. In this paper, I demonstrate through the tools of modern game theory, the instability of “stability for the right reasons.” Specifically, I will show that a well-ordered society can completely destabilize by the introduction of an arbitrarily small number of non- compliers whenever individuals fail to achieve (...) full common knowledge ever so slightly. (shrink)

Locke rejected anarchism. Locke defended the universal necessity of political governments on the grounds that the state of nature will occasionally generate the inconveniences of war. The standard interpretation of Locke identifies three main causes of war in the state of nature: the lack of a common judge, moral disagreement over the law of nature, and self-love. In this paper, I argue that the combination of these three factors does not guarantee that war will occur in every plausible scenarios of (...) Locke’s state of nature. Instead, in order for war to occur at least sometimes in every plausible scenario of Locke’s state of nature, there has to be some sort of epistemic deficit. In this paper, I show via the tools of modern game theory, how Locke’s state of nature may occasionally generate war by two kinds of epistemic problems implied by Locke’s own epistemology: disagreements in subjective probabilities, and uncertainty in other people’s moral motivation to use force to enforce the law of nature. The fact that war occurs primarily because of such epistemic problems suggests a role for a very limited form of government; namely, the ultra-ultra-minimal state, whose role is confined to solving such epistemic problems. (shrink)

Hobbes’s own justification for the existence of governments relies on the assumption that, without a government, our lives in the state of nature would result in a state of war of every man against every man. Many contemporary scholars have tried to explain why universal war is unavoidable in Hobbes’s state of nature by utilizing modern game theory. However, most game-theoretic models that have been presented so far do not accurately capture what Hobbes deems to be the primary cause of (...) conflict in the state of nature – which is uncertainty, rather than people’s egoistic psychology. Any game- theoretic model that does not incorporate uncertainty into the picture is, therefore, I claim, the wrong model. In this paper, I use Bayesian game-theory to show how universal conflict can break-out in the state of nature - even when the majority of the population would strictly prefer to cooperate and seek peace with other people - due to uncertainty about the other person’s type. Along the way, I show that the valuation of one’s own life is one of the central mechanisms that drives Hobbes’s pessimistic conclusion. (shrink)

Recently, philosophers have drawn on tools from game theory to explore behavior in Hobbes’ state of nature. I take a similar approach and argue the Lockean state of nature is best conceived of as a conflictual coordination game. I also discuss Nozick’s famous claim regarding the emergence of the state and argue the path to the minimal state is blocked by a hitherto unnoticed free-rider problem. Finally, I argue that on my representation of the Lockean state of nature both widespread (...) conflict and lasting peace are possible. This, I contend, is in line with one popular interpretation of Locke. (shrink)

Philosophers and social scientists have recently turned to game theory and agent-based models to better understand social contract formation. The stag hunt game is an idealization of social contract formation. Using the stag hunt game, we attempt to determine what, if any, barrier diversity is to the formation of an efficient social contract. We uncover a deep connection between tolerance, diversity, and the social contract. We investigate a simple model in which individuals possess salient traits and behave cooperatively when the (...) difference between their trait and the trait of their counterpart is less than their ‘tolerance level’. If traits are fixed and correspond to permanent or semipermanent features of the individual, such as religion or race, social contract formation is a remote possibility. If traits are malleable, social contract formation is possible but comes at the steep cost of diversity and tolerance, that is, individuals are unwilling to cooperate with those much different from themselves. Yet homogeneity and intolerance are not a long-term feature of the population. Over time mutations allow for increasingly tolerant agents to prosper, thereby ushering in trait diversity. In the end, all reap the benefits of cooperation. (shrink)

In this paper we use an experimental approach to investigate how linguistic conventions can emerge in a society without explicit agreement. As a starting point we consider the signaling game introduced by Lewis. We find that in experimental settings, small groups can quickly develop conventions of signal meaning in these games. We also investigate versions of the game where the theoretical literature indicates that meaning will be less likely to arise—when there are more than two states for actors to transfer (...) meaning about and when some states are more likely than others. In these cases, we find that actors are less likely to arrive at strategies where signals have clear conventional meaning. We conclude with a proposal for extending the use of the methodology of experimental economics in experimental philosophy. (shrink)

Conventions and leaders are believed to be the two pillars of justice and order in society. This paper evaluates this proposition and draws attention to two intriguing ways in which these pillars can malfunction. The argument is constructed by creating two new games, Greta’s Dilemma and the Incarceration Game. An awareness of these problems can help us use our ‘moral intention’ to reexamine our own collective behavior and to design prior conventions, which limit the power of the leader.

Hobbes believed that the state of nature would be a war of all against all. Locke denied this, but acknowledged that in the absence of government, peace is insecure. In this paper, I analyse both accounts of the state of nature through the lens of classical and experimental game theory, drawing especially on evidence concerning the effects of punishment in public goods games. My analysis suggests that we need government not to keep wicked or relentlessly self-interested individuals in line, but (...) rather to maintain peace among those who disagree about morality. (shrink)

Most business ethicists maintain that corporate actors are subject to a variety of moral obligations. However, there is a persistent and underappreciated concern that the competitive pressures of the market somehow provide corporate actors with a far-reaching excuse from meeting these obligations. Here, we assess this concern. Blending resources from the history of philosophy and strategic management, we demonstrate the assumptions required for and limits of this excuse. Applying the idea of ‘the state of nature’ from Thomas Hobbes, we suggest (...) that corporate actors would be excused from duties if complying with them threatened their vital interests. We show how this excuse is not available for most individuals within firms; instead, it is an excuse perhaps available to firms themselves, but only given substantive assumptions about corporate personhood. For those willing to make these assumptions, we apply the competitive advantage construct to delimit the scope of this excuse. We suggest that firms are excused from fulfilling an obligation when complying leads to a competitive disadvantage, as this imperils the firm’s vital interests. After revealing why this excuse does not generalize, we conclude by considering when we should reform the market to avoid the legitimacy of this excuse. (shrink)

In this paper we use an experimental approach to investigate how linguistic conventions can emerge in a society without explicit agreement. As a starting point we consider the signaling game introduced by Lewis. We find that in experimental settings, small groups can quickly develop conventions of signal meaning in these games. We also investigate versions of the game where the theoretical literature indicates that meaning will be less likely to arise---when there are more than two states for actors to transfer (...) meaning about and when some states are more likely than others. In these cases, we find that actors are less likely to arrive at strategies where signals have clear conventional meaning. We conclude with a proposal for extending the use of the methodology of experimental economics in experimental philosophy. (shrink)