Stationary, completely mixed and symmetric optimal and equilibrium strategies in stochastic games

Babu, Sujatha; Krishnamurthy, Nagarajan; Parthasarathy, T.

doi:10.1007/s00182-016-0555-5

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…The book by Washburn 9 is one such example. A similar case is found in Babu et al 12 They avoid to show that the Nash equilibrium, which they analyze, really is completely mixed. Babu et al 12 simply assume the existence of a particular probability vector.…”

Section: Introductionsupporting

confidence: 66%

“…A similar case is found in Babu et al 12 They avoid to show that the Nash equilibrium, which they analyze, really is completely mixed. Babu et al 12 simply assume the existence of a particular probability vector. In this paper, the existence of such a probability vector will be proved for a diagonal game matrix where all diagonal elements are strictly positive.…”

Section: Introductionsupporting

confidence: 66%

“…They are interested in model structure, selection and computation. Babu et al 12 give a good historical introduction to the literature on stochastic games. They also develop some new results in the area of equilibrium strategies of dynamic games based on mixed strategy assumptions within static games.…”

Section: Introductionmentioning

confidence: 99%

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Optimal decisions and expected values in two player zero sum games with diagonal game matrixes-explicit functions, general proofs and effects of parameter estimation errors

Lohmander

2019

IRATJ

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In this paper, the two player zero sum games with diagonal game matrixes, TPZSGD, are analyzed. Many important applications of this particular class of games are found in military decision problems, in customs and immigration strategies and police work. Explicit functions are derived that give the optimal frequences of different decisions and the expected results of relevance to the different decision makers. Arbitrary numbers of decision alternatives are covered. It is proved that the derived optimal decision frequency formulas correspond to the unique optimization results of the two players. It is proved that the optimal solutions, for both players, always lead to a unique completely mixed strategy Nash equilibrium. For each player, the optimal frequency of a particular decision is strictly greater than 0 and strictly less than 1. With comparative statics analyses, the directions of the changes of optimal decision frequences and expected game values as functions of changes in different parameter values, are determined. The signs of the optimal changes of the decision frequences, of the different players, are also determined as functions of risk in different parameter values. Furthermore, the directions of changes of the expected optimal value of the game, are determined as functions of risk in the different parameter values. Finally, some of the derived formulas are used to confirm earlier game theory results presented in the literature. It is demonstrated that the new functions can be applied to solve common military problems.

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Section: Introductionsupporting

confidence: 66%

Section: Introductionsupporting

confidence: 66%

See 1 more Smart Citation

Optimal decisions and expected values in two player zero sum games with diagonal game matrixes-explicit functions, general proofs and effects of parameter estimation errors

Lohmander

2019

IRATJ

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Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India

et al. 2020

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On Completely Mixed Stochastic Games

2022

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In this paper, we consider a two-person finite state stochastic games with finite number of pure actions for both players in all the states. In particular, for a large number of results we also consider one-player controlled transition probability and show that if all the optimal strategies of the undiscounted stochastic game are completely mixed then for $$\beta$$ β sufficiently close to 1; all the optimal strategies of $$\beta$$ β -discounted stochastic games are also completely mixed. A counterexample is provided to show that the converse is not true. Further, for single-player controlled completely mixed stochastic games if the individual payoff matrices are symmetric in each state, then we show that the individual matrix games are also completely mixed. For the non-zerosum single-player controlled stochastic game under some non-singularity conditions, we show that if the undiscounted game is completely mixed, then the Nash equilibrium is unique. For non-zerosum $$\beta$$ β -discounted stochastic games when Nash equilibrium exists, we provide equalizer rules for corresponding value of the game.

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Stationary, completely mixed and symmetric optimal and equilibrium strategies in stochastic games

Cited by 5 publications

References 27 publications

Optimal decisions and expected values in two player zero sum games with diagonal game matrixes-explicit functions, general proofs and effects of parameter estimation errors

Optimal decisions and expected values in two player zero sum games with diagonal game matrixes-explicit functions, general proofs and effects of parameter estimation errors

Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India

On Completely Mixed Stochastic Games

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