Stochastic games with endogenous transitions

We introduce a stochastic game in which transition probabilitiesdepend on the history of the play, i.e., the players’past action choices.To solve this new type of game under the limiting average reward crite-rion, we determine the set of jointly-convergent pure-strategy rewardswhich can be supported by equilibria involving threats.We examine the following setting for motivational and expositorypurposes. Each period, two agents exploiting a …shery choose betweencatching with restraint or without. The …sh stock is in either of twostates, High or Low, and in the latter each action pair yields lowerpayo¤s. Restraint is harmless to the …sh, but it is a dominated strategyin each stage game. Absence of restraint damages the resource, i.e.,the less restraint the agents show, the higher the probablities that Lowoccurs at the next stage of the play. This state may even become'absorbing', i.e., transitions to High become impossible.