Bayesian Strategy

In a Bayesian game, a pure strategy of player $i$ is a type-contingent action plan $$ s_i:T_i\to A_i. $$ It specifies what player $i$ will do after each type that player might observe.

A mixed or behavioral Bayesian strategy assigns to each type a distribution over actions: $$ \sigma_i:T_i\to\Delta(A_i). $$ A Bayesian strategy profile is a tuple of such type-contingent plans, one for each player.

References

• [MFoGT, Chapter 7, Section 7.4] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Strategies in Bayesian games are type-contingent plans.