[数学]演化博弈理论进化博弈论.ppt

Evolutionary Game Theory Outline EGT versus CGT Evolutionary Stable Strategies Concepts and Examples Replicator Dynamics Concepts and Examples Overview of 2 papers Selection methods, finite populations EGT v. Conventional Game Theory Models used to study interactive decision making. Equilibrium is still at heart of the model. Key difference is in the notion of rationality of agents. Agent Rationality In GT, one assumes that agents are perfectly rational. In EGT, trial and error process gives strategies that can be selected for by some force (evolution - biological, cultural, etc…). This lack of rationality is the point of departure between EGT and GT. Evolution When in biological sense, natural selection is mode of evolution. Strategies that increase Darwinian fitness are preferable. Frequency dependent selection. Evolutionary Game Theory (EGT) ESS Approach ESS = Nash Equilibrium + Stability Condition Notion of stability applies only to isolated bursts of mutations. Selection will tend to lead to an ESS, once at an ESS selection keeps us there. ESS - Definition ESS - Definition Standard Definition for ESS (Maynard Smith). I is an ESS if for all J ? I, E(I,I) ? E(J,I) and E(I,I) = E(J,I) ? E(I,J) E(J,J) where E is the payoff function . ESS - Definition ESS - Existence Let G be a two-payer symmetric game with 2 pure strategies such that E(s1,s1) ? E(s2,s1) AND E(s1,s2) ? E(s2,s2) then G has an ESS. ESS Existence If a c, then s1 is ESS. If d b, then s2 is ESS. Otherwise, ESS given by playing s1 with probability equal to (b-d)/[(b-d)+(a-c)]. ESS - Example 1 Consider the Hawk-Dove game with payoff matrix Nash equilibrium given by (7/12,5/12). This is also an ESS. ESS - Example 1 Bishop-Cannings Theorem: If I is a mixed ESS wi