Evolution in Symmetric Incomplete Information Games

The paper compares two models of evolution in symmetric two-player games with incomplete information. One model postulates that the type of a player is fixed, and evolution works within types. In the other model type-contingent strategies evolve. In the case of two types and two strategies it is shown that the stability properties of stationary states are the same under the two dynamics when payoffs do not depend on the type of the other player, but may differ when they do.incomplete information games, evolution, stability

Comparative Statics of Altruism and Spite

The equilibrium outcome of a strategic interaction between two or more people may depend on the weight they place on each other’s payoff. A positive, negative or zero weight represents altruism, spite or complete selfishness, respectively. Paradoxically, the real, material payoff in equilibrium for a group of altruists may be lower than for selfish or spiteful groups. However, this can only be so if the equilibria involved are unstable. If they are stable, the total (equivalently, average) payoff can only increase or remain unchanged with an increasing degree of altruism.Altruism, spite, comparative statics, strategic games, stability of equilibrium

Stochastic Game Theory: Adjustment to Equilibrium Under Noisy Directional Learning

This paper presents a dynamic model in which agents adjust their decisions in the direction of higher payoffs, subject to random error. This process produces a probability distribution of players' decisions whose evolution over time is determined by the Fokker-Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studied games. In equilibrium, the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs. This "logit equilibrium" forms a stochastic generalization of the Nash equilibrium and provides a possible explanation of anomalous laboratory data.bounded rationality, noisy directional learning, Fokker- Planck equation, potential games, logit equilibrium, stochastic potential.

Evolutionarily Stable Correlation

Most existing results of evolutionary games restrict only to the Nash equilibrium. This paper introduces the analogue of evolutionarily stable strategy (ESS) for correlated equilibria. We introduce a new notion of evolutionarily stable correlation (ESC) and prove that it generalizes ESS. We also study analogues of perfection (cf. Dhillon and Mertens (1994)), properness, and replicator dynamics for the correlation equilibrium and discuss their relationships with ESCCorrelated Equilibrium, Evolutionarily Stable Correlation, Evolutionarily Stable State, Random Device

A general model of best response adaptation

We develop a general model of best response adaptation in large populations for symmetric and asymmetric conflicts with role-switching. For special cases including the classical best response dynamics and the symmetrized best response dynamics we show that the set of Nash equilibria is attracting for zero-sum games. For asymmetric conflicts and equally large populations, convergence to a Nash equilibrium in the base game implies convergence to a Nash equilibrium on the Wright manifold in the role game.Role Games, Best Response Adaptation, Learning, Evolution

Evolutionary Game Theory and Thorstein Veblen’s Evolutionary Economics: Is EGT Veblenian?

This essay provides an approach to the analysis of the link between Thorstein Veblen's evolutionary approach and evolutionary game theory (EGT). We shed some light on the potential contribution of Veblen's theory of socioeconomic evolution to the discussion on the application of EGT to social environments. We also investigate to what extent elements of EGT can be used to formalize some of the basic evolutionary principles proposed by Veblen. The methodological imperatives laid down by Veblen, defining an evolutionary approach, are presented. We provide an analytical framework that allows the evaluation of EGT in terms of Veblen's evolutionary approach. To better understand the main principles and rationale behind EGT and how it can be applied as a tool for analyzing issues on the diversity, interaction, and evolution of social systems, we discuss this nontraditional approach and its basic concepts. Finally, the main characteristics of EGT are contrasted with Veblen's principles.Evolution; Evolutionary Economics; Evolutionary; Game Theory; Games

A Dynamic Model of Reciprocity with Asymmetric Equilibrium Payoffs

We analyze indirect evolutionary two-player games to identify the dynamic emergence of (strong) reciprocity in a large number of economic settings. The underlying evolutionary environment allows for an arbitrary initial population state provided that every degree of the compact space of reciprocity is adherent to at least one individual of the corresponding continuum population. The basic results, which essentially maintain the evolutionary viability of reciprocity, are, in several directions, context dependent, and minimum valid for the wide class of evolutionary dynamics which hold for regularity and payoff-monotonicity. The evolutionary solution concept which is applied to elevate the explanatory power of emerging Nash equilibria is dominance solvability, in this case, for continuous strategy spaces. An asymmetric aspect comes into play since the actions of the evolutionary players are not only determined by the current state of reciprocity but also by their inherent, context-free preferences towards others which differ among one another devoid of being endogenized in the time span of the dynamic process at hand.reciprocity, evolutionary game theory, dominance solvability, asymmetric game setting, payoff-monotonic dynamics