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Computing a mechanism for a Bayesian and partially observable Markov approach

Clempner Julio B., Poznyak Alexander S.

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 3

463--478

The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.

A game theoretical study of generalised trust and reciprocation in Poland. I. Theory and experimental design

Markowska-Przybyła U., Ramsey D.

Operations Research and Decisions

2014

Vol. 24, No. 3

59--76

Although studies using experimental game theory have been carried out in various countries, no such major study has occurred in Poland. The study described here aims to investigate generalised trust and reciprocation among Polish students. In the literature, these traits are seen to be positively correlated with economic growth. Poland is regarded as the most successful post-soviet bloc country in transforming to a market economy but the level of generalised trust compared to other postcommunist countries is reported to be low. This study aims to see to what degree this reported level of generalised trust is visible amongst young Poles via experimental game theory, along with a questionnaire. The three games to be played have been described. Bayesian equilibria illustrating behaviour observed in previous studies have been derived for two of these games and the experimental procedure has been described.