When and how much the altruism impacts your privileged information? Proposing a new paradigm in game theory: The boxers game

TL;DR

This paper introduces a new N-player game modeling how altruism influences the value of privileged information, combining elements from public goods and minority games, with analytical and simulation results.

Contribution

It proposes a novel game framework incorporating altruism and privileged information, analyzing its impact through analytical and numerical methods.

Findings

Altruism can significantly affect the value of privileged information.

Positive payoff regions depend on altruism and information density.

Evolutionary strategies can diminish the gains of informed players.

Abstract

In this work, we proposed a new $N$-person game in which the players can bet on two options, for example represented by two boxers. Some of the players have privileged information about the boxers and part of them can provide this information to uninformed players. However, this information may be true if the informed player is altruist or false if he is selfish. So, in this game, the players are divided in three categories: informed and altruist players, informed and selfish players, and uninformed players. By considering the matchings ($N/2$ distinct pairs of randomly chosen players) and that the payoff of the winning group follows aspects captured from two important games, the public goods game and minority game, we showed quantitatively and qualitatively how the altruism can impact on the privileged information. We localized analytically the regions of positive payoffs which were corroborated by numerical simulations performed for all values of information and altruism densities given that we know the information level of the informed players. Finally, in an evolutionary version of the game ,we showed that the gain of the informed players can get worse if we adopted the following procedure: the players increase their investment for situations of positive payoffs, and decrease their investment when negative payoffs occur.