How do you solve this zero-sum game? If it's symmetric, do you assign equal probability (1/5) to each strategy to find an optimal strategy and to find the game value?
2026-04-13 05:03:50.1776056630
Zero Sum Games and Symmetry
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This particular kind of a zero-sum game matrix fits to a Latin square game definition as described here (Section 2.5). The strategy for choosing every strategy with an equal probability is an equilibrium and the value of the game is the average of the value in every row/column. For more intuition you can refer to a matching pennies game which is special case.
I think you can prove that there are no other equilibria with all strategies mixed by proving that there is no other set of strategies to equate all 5 strategies for the other player. And it's also easy to see that there are no equilibria with zero probability assigned to one of the strategies since the opponent would just get the maximum possible payoff with certainty.