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The Complete Idiot's Guide to Game Theory by Edward Rosenthal, Ph.D., Edward C. Rosenthal

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Solving Zero Sum Games

It’s time to move up to the big leagues: to solve zero sum games in general. Most such games do not have equilibrium solutions in pure strategies, so we need to come up with the right mixed strategies.

Mixed Strategy Equilibria

Before we go any further, scan the converted zero sum network game for dominant strategies. If you didn’t find any, that’s good, because no strategy is dominant. This means that both players will have to resort to some sort of mixing, or random picking, of their strategies. Before working through the solution mathematically, here are the key steps to the analysis:
1. Each player figures out what their average payoff is under each of the other player’s pure strategies and writes that down.
2. ...

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