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Showing posts from January, 2019

Have you heard of Berge equilibrium? And should you have?

Recently I refereed a paper on the existence of Berge equilibrium. I must confess that until reading the paper I knew nothing of Berge equilibrium. But in my defence, the equilibrium does not get a mention in any game theory textbook on my shelves and, surely most telling of all, does not get an entry in Wikipedia. So, what is Berge equilibrium and should we hear more about it? The origins of the equilibrium are a book by French mathematician Claude Berge (who does get a Wikipedia page) on a general theory of n-person games, first published in 1957. But it has seemingly gone pretty much unnoticed from then on, although there is a growing literature on the topic as summarized in a 2017 paper by Larbani and Zhukovskii. The basic idea behind Berge equilibrium seems to be one of altruism or cooperation between players in a group. To explain, consider a game. Let s i denote the strategy of player i, s -i the strategies of everyone other than i and u i (s i , s -i ) the payoff of play