In the previously cited example (Table-1), the increase in the prices of organizations’ products is the best strategy for both of them. Therefore, it is regarded as the best strategy for every player of the game. In other words, a pure strategy is the one that provides maximum profit or the best outcome to players. In a pure strategy, players adopt a strategy that provides the best payoffs. In the following article, we will look at how to find mixed strategy Nash equilibria, and how to interpret them. But how often should you mix your strategy and serve to each side to minimize your opponent’s chances of winning? Calculating these probabilities would give us our mixed strategy Nash equilibria, or the probabilities that each strategy is used which would minimize the opponent’s expected payoff. If you serve to the backhand 100% of the time, it would be easy for the opponent to catch on and return from the backhand side more often than the forehand, maximizing his expected payoff. It is apparent to you that a pure strategy would be exploitable. Given these pure strategy payoffs, we can calculate the mixed strategy payoffs by figuring out the probability each strategy is chosen by each player. The payoffs to each player for every action are given in pure strategy payoffs, as each player is only guaranteed their payoff given the opponent’s strategy is employed 100% of the time. This gives us the payoffs when the returner receives the serve correctly ( F S ,F R or B S ,B R), or incorrectly ( F S ,B R or B S ,F R). For the returner, the strategies F R and B R are observed when the returner moves to the forehand or backhand side to return the serve, respectively. The strategies F S or B S are observed for the server when the ball is served to the side of the service box closest to the returner’s forehand or backhand, respectively. Observe the following hypothetical in the payoff matrix: In this scenario, assume each player has two strategies (forehand F, and backhand B). In the game of tennis, each point is a zero-sum game with two players (one being the server S, and the other being the returner R). For this article, we shall say that pure strategies are not mixed strategies. This means that in a way, a pure strategy can also be considered a mixed strategy at its extreme, with a binary probability assignment (setting one option to 1 and all others equal to 0). The definition of a mixed strategy does not rule out the possibility for an option(s)to never be chosen (eg. In other words, a person using a mixed strategy incorporates more than one pure strategy into a game. Using the example of Rock-Paper-Scissors, if a person’s probability of employing each pure strategy is equal, then the probability distribution of the strategy set would be 1/3 for each option, or approximately 33%. Mixed strategyĪ mixed strategy is an assignment of probability to all choices in the strategy set. rock, paper, and scissors) available in this game is known as the strategy set. The probability for choosing scissors equal to 1 and all other options (paper and rock) is chosen with the probability of 0. For example, in the game of Rock-Paper-Scissors,if a player would choose to only play scissors for each and every independent trial, regardless of the other player’s strategy, choosing scissors would be the player’s pure strategy. A pure strategy is an unconditional, defined choice that a person makes in a situation or game.
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