Abstract
This paper deals with application of game theory model to insur- ance market. We observed a form of mutual insurance in conditions of full and partial information obtained by insurance buyers. First part of the paper defines the model of non-cooperative game, fol- lowed by principles of optimality, types of stability and equilibrium. Here, model of non-cooperative game has been analyzed under the assumption that players are fully informed. Situation where players are only partially informed requires model which takes into account decision process and analysis of every player's actions. This analy- sis requires that hierarchical structure among players need to be established. Model of conflict situation, with established hierar- chical structure with informational reflexivity, represent the model of reflexive game. We define that reflexive game model, followed by required conditions for which some strategy is informational equilib- rium strategy. We then proceed to perform analysis of game theo- retic application to mutual insurance model, with hierarchical struc- ture in agent positioning, in conditions of both full and partial infor- mation obtained by the player, with the goal of finding equilibrium strategies.
Highlights
Development of game theory provided lots of opportunity to more accurately model variety of economic phenomena in observed system
We observed a form of mutual insurance in conditions of full and partial information obtained by insurance buyers
Theory of non-cooperative games starts with an assumption that the decision maker is a rational individual that aspires to the best possible outcome in accordance with pre-defined rules
Summary
Development of game theory provided lots of opportunity to more accurately model variety of economic phenomena in observed system. Theory of non-cooperative games starts with an assumption that the decision maker (player) is a rational individual that aspires to the best possible outcome (maximizing utility) in accordance with pre-defined rules. Milgrom, Roberts, and Wilson in their experiment of finite game of repetition came to conclusion that players deviate from dominant strategies in some periods of the game, and they aspire to certain level of cooperation Due to that they analyze repetition model with partial information. In addition to models mentioned, game theory models are being introduced, especially in situations when insurance companies include subadditive insurance premiums for independent risks In such cases, individual players can protect their premiums by partaking in mutual insurance, rather than individual. Power and Shubik (1998, 2006) analyze the effect of insurants number and optimal number of reinsured agents, whereas Taksak and Zeng (2011) analyze disproportionate reinsurance
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