5.1 Bayesian Game

Game of Incomplete Information (Bayesian Game)

A Bayesian game is a game in which players do not know some relevant characteristics of their opponents, which may include:

• Their payoffs.
• Their available options.
• Their beliefs.

In a Bayesian game, player $i\in N$‘s preferences are represented by a set $T_i$ known as $i$‘s type space, known by all players in the game. Each element $t_i\in T_i$ is a single type of player $i$, not known by any of the other players $j\in N\backslash i$.

Furthermore, a player’s strategy gives a choice of some $s_i\in S_i$ for each type $t_i\in T_i$.

Static Bayesian Game

Dynamic Bayesian Game