"On Detail-Free Mechanism Design and Rationality"

The study of mechanism design is sometimes criticized, because the designed mechanisms depend on the fine detail of the model specification, and agents' behavior relies on the strong common knowledge assumptions on their rationality and others. Hence, the study of 'detail-free' mechanism design with weak informational assumptions is the most important to make as the first step towards a practically useful theory. This paper will emphasize that even if we confine our attentions to detail-free mechanisms with week rationality, there still exist a plenty of scope for development of new ideas on how to design a mechanism to play the powerful role. We briefly explain my recent works on this line, and argue that the use of stochastic decision works much in large exchange economics, and agents' moral preferences can drastically improve implementability of social choice functions.

On Detail-Free Mechanism Design and Rationality

The study of mechanism design is sometimes criticized, because the designed mechanisms depend on the fine detail of the model specification, and agents' behavior relies on the strong common knowledge assumptions on their rationality and others. Hence, the study of 'detail-free' mechanism design with weak informational assumptions is the most important to make as the first step towards a practically useful theory. This paper will emphasize that even if we confine our attentions to detail-free mechanisms with week rationality, there still exist a plenty of scope for development of new ideas on how to design a mechanism to play the powerful role. We briefly explain my recent works on this line, and argue that the use of stochastic decision works much in large exchange economics, and agents' moral preferences can drastically improve implementability of social choice functions.

Game theory

game theory

The Evolution of Coordination under Inertia

This paper models the phenomenon of inertia driven by individual strategy switching costs in a stochastic evolutionary context. Kandori, Mailath, and Rob's (1993) model of a finite population of agents repeatedly playing a 2x2 symmetric coordination game is extended to allow for such inertia. Taking noise to the limit, a number of new short- to medium-run equilibria emerge, centred around the mixed-strategy equilibrium. Thus, unusually, an evolutionary model is seen to provide some justification for the controversial concept of mixed-strategy equilibrium. However, Kandori, Mailath, and Rob's long-run selection of the risk-dominant equilibrium continues to hold, both under fixed-rate mutations and under state-dependent mutations driven by stochastic switching costs. The key to this is the satisfaction of Blume's (1999) "skew-symmetry" of the noise process, which is shown to be crucial even under simultaneous strategy revisions. In fact, the presence of the new short-run equilibria can under certain conditions serve to reduce the expected waiting time before the risk-dominant equilibrium is reached - an instance of Ellison's (2000) idea that evolution is more rapid when it can proceed via a series of small "steps" between extremes. This suggests inertia to be a surprisingly efficient phenomenon, and also serves to moderate the force of the Ellison (1993) critique of excessively long transition times in models with vanishing noise.

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

The Evolution of Conflict under Inertia

In Norman (2003), the introduction of individual strategy switching costs, and thus inertia, into stochastic evolutionary coordination games was found inter alia to strengthen the mixed-strategy equilibrium as a short- to medium-run equilibrium. This paper considers the impact of such switching costs on the conflict scenario of Hawk-Dove games. The "attractive" mixed-strategy equilibrium of Hawk-Dove games represents a far better candidate for long-run equilibrium than its unstable counterpart in coordination games, and yet robust selection results have proved elusive, with conditions on the selection dynamics generally being required. Such a condition remains a necessity in the switching cost model with state-independent mutations. However, a more realistic model of state-dependent mutations driven by stochastic switching costs overcomes this problem, and identifies a threshold mean switching cost, above which the mixed-strategy equilibrium is selected in the long run for a wide class of switching cost distributions.