Abstract. Experimentalists frequently claim that human subjects in the laboratory violate game-theoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very definition of a game and of players ’ preferences, in particular with respect to potential context dependence, interpersonal preference dependence, backward induction and incomplete information.

Existing task allocation and scheduling algorithms, including taskallocation algorithms for multi-robot systems, generally assume that tasks are independent. This assumption is often violated in groups of cooperative mobile robots, where the group dynamics can have a critical impact on performance. We present a multi-robot task allocation algorithm that is sensitive to group dynamics. Our algorithm is based on vacancy chains, a resource distribution process common in human and animal societies. We study the problem of cooperative transportation in simulation. We demonstrate through experiments in simulation that if robots keep local task utility estimates, and follow a greedy task selection policy, the interactions in the group cause the collection of learned policies to converge toward an optimal allocation pattern as defined by the vacancy chain framework. As the robots are continuously updating their individual utility estimates, the vacancy chain algorithm has the additional property of adapting automatically to changes in the environment, e.g., robot breakdowns or changes in task values. Our experiments show that in the case of such changes, the vacancy chain algorithm consistently outperforms random and static task allocation algorithms. Finally, the vacancy chain algorithm uses no communication or unique roles, and as a result it is more likely to scale to large groups and will degrade gracefully in response to individual breakdowns.

We offer a definition of iterated elimination of strictly dominated strategies (IESDS ∗ ) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS ∗ is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS ∗ by means of a “stability ” criterion, and offer a sufficient and necessary epistemic condition for IESDS ∗.Weshowbyanexample that IESDS ∗ may generate spurious Nash equilibria in the class of Reny’s better-reply secure games. We provide sufficient/necessary conditions under which IESDS ∗ preserves the set of Nash equilibria. JEL Classification: C70, C72.

Static stability of equilibrium in strategic games differs from dynamic stability in not being linked to any particular dynamical system. In other words, it does not make any assumptions about off-equilibrium behavior. Examples of static notions of stability include evolutionarily stable strategy (ESS) and continuously stable strategy (CSS), both of which are meaningful or justifiable only for particular classes of games, namely, symmetric multilinear games or symmetric games with a unidimensional strategy space, respectively. This paper presents a general notion of local static stability, of which the above two are essentially special cases. It is applicable to virtually all

Static stability in strategic games differs from dynamic stability in only considering the players ’ incentives to change their strategies. It does not rely on any assumptions about the players ’ reactions to these incentives and it is thus independent of the law of motion (e.g., whether players move simultaneously or sequentially). Examples of static notions of stability include evolutionarily stable strategy (ESS) and continuously stable strategy (CSS), both of which are meaningful or justifiable only for particular classes of symmetric and population games, such as games with multilinear payoff functions or with unidimensional strategy spaces. This paper presents a general notion of static stability in symmetric (-player) games and population games and with non-discrete strategy spaces, of which ESS and CSS are essentially special cases. JEL Classification: C72.

this paper, we suggest using ideas and techniques derived from CAS to enable the construction of resilient, scalable, self-organizing and self-repairing distributed systems as ensembles of autonomous agents that mimic the behavior of some natural or biological process. It is our belief that this approach o#ers a chance for application developers to meet the increasing challenges arising in dynamic network settings and obtain desirable global properties such as resilience, scalability and adaptability, without explicitly programming them into the individual agents

Fixed points of the (most) refined best-reply correspondence, introduced in Balkenborg, Hofbauer, and Kuzmics (2009), in the agent normal form of extensive form games have a remarkable, one might call subgame consistency property. They automatically induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense fixed points of this correspondence refine even trembling-hand perfect equilibria, while, on the other hand, reasonable equilibria that are not even weak perfect Bayesian are fixed points of this correspondence.

This paper provides an in-depth study of the (most) refined best-reply correspondence introduced by Balkenborg, Hofbauer, and Kuzmics (2009a). We study notions of strict and weak dominance most appropriate to it, its fixed points, and rationalizability based on it, and how these concepts are related to well-known concepts such as, among others, Selten’s (1975) trembling-hand perfection, Kalai and Samet’s (1984) persistent equilibria, and various

This paper analyzes a stochastic model of evolution in normal form games. The long-run behavior of individuals in this model is investigated in the limit where mutation rates tend to zero, while the expected number of mutations, and hence population sizes, tend to infinity. It is shown that weakly dominated strategies do not survive evolution. Also strategies which are not rationalizable in the game obtained from the original game by the deletion of all weakly dominated strategies disappear in the long-run. Furthermore it is shown that if evolution leads to a unique prediction this prediction must be equivalent to a trembling-hand perfect equilibrium.

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it (1) has a product structure, (2) is upper hemi–continuous, (3) always includes a best reply to any mixed strategy profile, and (4) is convex- and closed-valued. For each generalized best reply correspondence, we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of point-wise set inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on point-wise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We find that every persistent retract (Kalai and Samet 1984) contains an MASF. Furthermore, persistent retracts are minimal CURB sets (Basu and Weibull 1991) based on the refined best reply correspondence. Conversely, every MASF must be a prep set (Voorneveld 2004), based again, however, on the refined best reply correspondence.