We consider the problem of fair allocation in economies with indivisible goods. Our primary concept is that of an envy-free allocation, that is, an allocation such that no agent would prefer anyone else's bundle to his own. Since there typically is a large set (a continuum) of such allocations, the need arises to identify well-behaved selections from the no-envy solution. First we establish the non-existence of ‘population monotonic’ selections. Then we propose a variety of selections motivated by intuitive considerations of (...) fairness. (shrink)

Two examples demonstrate the possibility of extremely complicated non-convergent behavior in evolutionary game dynamics. For the Taylor-Jonker flow, the stable orbits for three strategies were investigated by Zeeman. Chaos does not occur with three strategies. This papers presents numerical evidence that chaotic dynamics on a strange attractor does occur with four strategies. Thus phenomenon is closely related to known examples of complicated behavior in Lotka-Volterra ecological models.

We calculate the Lebesgue–measures of the stability sets of Nash-equilibria in pure coordination games. The results allow us to observe that the ordering induced by the Lebesgue–measure of stability sets upon strict Nash-equilibria does not necessarily agree with the ordering induced by risk–dominance. Accordingly, an equilibrium selection theory based on the Lebesgue–measure of stability sets would be necessarily different from one which uses the Nash-property as a point of orientation.

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instance, a full appreciation of Axelrod's The Evolution of Cooperation requires that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questions we re-examine the very foundations of the evolutionary model. The results of this paper can be analytically separated into three parts. (...) The first part is conceptual: it identifies the evolutionary model's assumptions and shows how different assumptions imply different types of evolutionary stability. The second part is deductive: it establishes necessary and sufficient conditions for the types of evolutionary stability identified in the first part, and demonstrates in which games these kinds of stability can (and cannot) be attained. The third and final part is applied: it relates the general findings (which are independent of the specific payoffs of any particular evolutionary game) to the issue of the evolutionary stability of cooperation. Results on cooperation appear throughout the paper as they both exemplify and motivate the general results. These results essentially explain when cooperation is and is not stable, and why, thus shedding new light on the meaning and applicability of Axelrod's widely known claims. (shrink)

The paper is essentially a short version Spohn "Strategic Rationality" which emphasizes in particular how the ideas developed there may be used to shed new light on the iterated prisoner's dilemma (and on iterated Newcomb's problem).

The backward induction argument purports to show that rational and suitably informed players will defect throughout a finite sequence of prisoner's dilemmas. It is supposed to be a useful argument for predicting how rational players will behave in a variety of interesting decision situations. Here, I lay out a set of assumptions defining a class of finite sequences of prisoner's dilemmas. Given these assumptions, I suggest how it might appear that backward induction succeeds and why it is actually fallacious. Then, (...) I go on to consider the consequences of adopting a stronger set of assumptions. Focusing my attention on stronger sets that, like the original, obey the informedness condition, I show that any supplementation of the original set that preserves informedness does so at the expense of forcing rational participants in prisoner's dilemma situations to have unexpected beliefs, ones that threaten the usefulness of backward induction. (shrink)

This article argues that evolutionary models based on selection validate, under appropriate conditions, the relevance of optimality as an explanatory mechanism in rational choice theory. The reason is that these frameworks share the mechanism that drives the results, namely, optimization, even if they situate it at different levels. The consequences of our argument are twofold. First, it resolves the tension between those predictions of rational choice theory that are accurate and the evidence showing that individuals seldom optimize. Second, it relativizes (...) the explanatory import of rationality without diminishing the role of optimization as a mechanism. (shrink)

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to enrich (...) the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)

even if an equilibrium is asymptotically stable, that is no guarantee that the system will reach that equilibrium unless we know that the system's initial state is sufficiently close to the equilibrium. Global stability of an equilibrium, when we have it, gives the equilibrium a much more powerful explanatory role. An equilibrium is globally asymptotically stable if the dynamics carries every possible initial state in the interior of the state space to that equilibrium. If an equilibrium is globally stable, it (...) can have.. (shrink)

I model an attempt by radical parties to topple a modus vivendi between a ruling government and a moderate opposition group. Cooperation between the regime and the moderate opposition is possible if each player prefers mutual cooperation to mutual confrontation. If each player also prefers mutual confrontation to cooperating while the other defects then radical parties have a chance at breaking up this accord. Radical parties can succeed in bringing the government and opposition to mutual confrontation if they can agree (...) on power-sharing arrangements after regime change. This paper also resolves central questions surrounding the trial and crucifixion of Jesus Christ. I use an institutional approach to infer player preferences from historical and biblical sources and then use game theory to model the interactions between participants in these events. In so doing, I clarify aspects of the Gospel narrative that have puzzled readers for the past 2000 years. (shrink)

Much of the history of game theory has been dominated by the problem of indeterminacy. The very search for better versions of rationality, as well as the long list of attempts to refine Nash equilibrium, can be seen as answers to the indeterminacy that has accompanied game theory through its history. More recently, the experimental approach to game theory has attempted a more radical solution: by directly generating a stream of behavioral observations, one hopes that behavioral hypotheses will be sharper, (...) and predictions more accurate. This article looks at several attempts to address indeterminacy, including the shift to evolutionary models. However, because its goal is to establish whether rational choice models are inescapably doomed to produce indeterminate outcomes, it pays much more attention to the experimental turn in game theory, the difficulty it encounters, and the promising results obtained by more realistic models of rationality that include a social component. (shrink)