<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A method of solving a three-person game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous. The method is based on stacking equilibria of “short” three-person games, each defined on an interval where the pure strategy value is constant. In the case of finite three-person games, which factually are trimatrix games, the equilibria are considered in general terms, so they can be in mixed strategies as well. The stack is any interval-wise combination (succession) of the respective equilibria of the “short” trimatrix games. Apart from the stack, there are no other equilibria in this “long” trimatrix game. An example is presented to show how the stacking is fulfilled for a case of when every “short” trimatrix game has a pure-strategy equilibrium. The presented method, further “breaking” the initial “long” game defined on a product of staircase-function finite spaces, is far more tractable than a straightforward approach to solving directly the “long” trimatrix game would be.</p>
</abstract>

A method of solving a three-person game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous. The method is based on stacking equilibria of “short” three-person games, each defined on an interval where the pure strategy value is constant. In the case of finite three-person games, which factually are trimatrix games, the equilibria are considered in general terms, so they can be in mixed strategies as well. The stack is any interval-wise combination (succession) of the respective equilibria of the “short” trimatrix games. Apart from the stack, there are no other equilibria in this “long” trimatrix game. An example is presented to show how the stacking is fulfilled for a case of when every “short” trimatrix game has a pure-strategy equilibrium. The presented method, further “breaking” the initial “long” game defined on a product of staircase-function finite spaces, is far more tractable than a straightforward approach to solving directly the “long” trimatrix game would be.

Equilibrium stacks for a three-person game on a product of staircase-function continuous and finite strategy spaces

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A method of solving a three-person game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous. The...

Equilibrium stacks for a three-person game on a product of staircase-function continuous and finite strategy spaces

Published Online: Feb 23, 2022

Page range: 27 - 64

Received: Jun 07, 2021

Accepted: Dec 04, 2021

DOI: https://doi.org/10.2478/fcds-2022-0002

Keywords
game theory, payoff functional, staircase-function strategy, three-person game, trimatrix game

© 2022 Vadim Romanuke, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Equilibrium stacks for a three-person game on a product of staircase-function continuous and finite strategy spaces

Published Online: Feb 23, 2022

Page range: 27 - 64

Received: Jun 07, 2021

Accepted: Dec 04, 2021

DOI: https://doi.org/10.2478/fcds-2022-0002

Keywordsgame theory, payoff functional, staircase-function strategy, three-person game, trimatrix game

© 2022 Vadim Romanuke, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
game theory, payoff functional, staircase-function strategy, three-person game, trimatrix game