Equilibrium in a stochastic $n$-person game

Fink, A. M.

doi:10.32917/hmj/1206139508

Cited by 213 publications

(147 citation statements)

References 2 publications

Supporting

Mentioning

146

Contrasting

Unclassified

Order By: Relevance

“…Such results have also been extended to non-zero-sum stochastic games (Fink, 1964, Takahashi, 1964, Sobel, 1971) and also to stochastic games with infinite state space and infinite action space (Maitra and Parthasarathy, 1970). Maitra and Sudderth (1996) proposed an alternative proof of the existence of value in the finite, undiscounted, zero-sum case which extends to the case when the state space is uncountable as well.…”

Section: Introductionmentioning

confidence: 94%

Orderfield property of mixtures of stochastic games

Krishnamurthy

Parthasarathy

Ravindran

2010

Sankhya

View full text Add to dashboard Cite

We consider certain mixtures, Γ, of classes of stochastic games and provide sufficient conditions for these mixtures to possess the orderfield property. For 2-player zero-sum and non-zero sum stochastic games, we prove that if we mix a set of states S1 where the transitions are controlled by one player with a set of states S2 constituting a sub-game having the orderfield property (where S1 ∩ S2 = ∅), the resulting mixture Γ with states S = S1 ∪ S2 has the orderfield property if there are no transitions from S2 to S1. This is true for discounted as well as undiscounted games. This condition on the transitions is sufficient when S1 is perfect information or SC (Switching Control) or ARAT (Additive Reward Additive Transition). In the zero-sum case, S1 can be a mixture of SC and ARAT as well. On the other hand,when S1 is SER-SIT (Separable Reward -State Independent Transition), we provide a counter example to show that this condition is not sufficient for the mixture Γ to possess the orderfield property. In addition to the condition that there are no transitions from S2 to S1, if the sum of all transition probabilities from S1 to S2 is independent of the actions of the players, then Γ has the orderfield property even when S1 is SER-SIT. When S1 and S2 are both SER-SIT, their mixture Γ has the orderfield property even if we allow transitions from S2 to S1. We also extend these results to some multi-player games namely, mixtures with one player control Polystochastic games. In all the above cases, we can inductively mix many such games and continue to retain the orderfield property.

show abstract

Section: Introductionmentioning

confidence: 94%

Orderfield property of mixtures of stochastic games

Krishnamurthy

Parthasarathy

Ravindran

2010

Sankhya

View full text Add to dashboard Cite

show abstract

“…For countable state spaces a variety of existence theorems for Markov equilibria have been established by, e.g., Shapley (1953), Fink (1964), and Federgruen (1978). The existence of homogeneous Markov equilibria has also been proved in special cases with uncountable state spaces.…”

Section: Introductionmentioning

confidence: 97%

Stationary equilibria in discounted stochastic games with weakly interacting players

Horst¹

2005

Games and Economic Behavior

View full text Add to dashboard Cite

“…The sets of actions and types are finite. The existence of a communication equilibrium then follows from standard arguments (existence of Nash equilibria for discounted stochastic games, Fink, 1964;Mertens and Parthasarathy, 1991), using compactness of strategy sets and continuity of payoff functions in the product topology.…”

Section: A33 Existence Of An Equilibriummentioning

confidence: 99%