A constructive study of Markov equilibria in stochastic games with strategic complementarities

Stationary Markov perfect equilibria in discounted stochastic games

“…All these papers impose special conditions on the payoff functions and state transitions 4. Additional ergodic properties were obtained in[10] under stronger conditions 5. An error in the relevant example of[27] was pointed out in[28], and a new example was presented therein.…”

On the Computation of Value Correspondences for Dynamic Games

“…These alternatives provide direct characterization of specific sub-game perfect equilibria in certain settings. Examples include Herings and Peeters [11] who provide a homotopy method for computing stationary equilibria in dynamic games and Balbus et al [4] who show how to calculate extremal Markov equilibria in stochastic games with complementarities. We mention also Feng et al [9] who use a similar approach to us to characterize equilibria in economies with distortions and taxes.…”

“…with an inherited pair of state variables (s t , k t ) ∈ S × K , where S is finite and K ⊂ R N is compact. 4 The former is a shock and evolves according to a Markov chain with transition ; the latter is an endogenous state whose evolution is defined below. On entering period t, the agents simultaneously select a profile of actions a t = {a i t } I i=1 , with each agent i choosing his or her action a i t from a compact set A i (s t , k t ) ⊂ R D .…”

Elementary Subpaths in Discounted Stochastic Games

“…They have been introduced in a seminal paper by Shapley [47], and they can be applied, e.g., in industrial organization [23,43], taxation [44], fish wars, stochastic growth models, communication networks, queues, and hiding and searching for army forces; see the references in [5,9,21,25]. The stochastic game model extends both Markov decision processes (MDPs) which have only a single decision maker and repeated games where the players encounter the same game over and over again.…”

“…Sleet and Yeltekin [48], Yeltekin [53] compute correlated subgame-perfect equilibria that need not be Markovian using lower and upper bounds. Balbus et al [9] provide a constructive method for finding stationary Markov strategies in uncountable state spaces where APS-type methods may fail. Feng et al [24] find Markov equilibria in a model with short-run players.…”