To make the husband indifferent between the two strategies, we need to set -20p + 10 = 0, which leaves us with p = 1⁄2. Then, the expected payoff to the husband for cheating openly is (-10)(p) + (10)(1-p), which equals to -20p + 10, while the expected payoff to the husband for secretly cheating is (0)(p) + (0)(1-p), which equals 0. Next, the wife chooses a probability of p for catching her husband cheat C. To make the wife indifferent between the two strategies, we need to set 20q=10, which leaves us with q =1/2. Then, the expected payoff to the wife for strategy catch cheating C is (20)(q) + (0)(1-q), which equals 20q, while the expected payoff to the wife for ignore cheating is (10)(q) + (10)(1-q), which equals 10. First, the husband chooses a probability of q for cheating openly O. In a mixed strategy equilibrium, in order to make the player indifferent between the two strategies, it must be the case that the payoff from one strategy (let’s say catch cheating C) is equal to the payoff from the other strategy (let’s say cheat openly O). Thus, letting 1-p be the probability that the wife ignores the cheating (I), and 1-q being the probability that the husband secretly cheats (S). Using the principle of indifference in the textbook, I let p be the probability that the wife catches him cheating (C), and I let q be the probability that the husband openly cheats on his wife (O). However, we can find a mixed-strategy equilibrium. Again, we see that these are not best responses to each other. However, if the husband were to cheat openly (O), then the wife would choose to catch him cheating (C). Likewise, if the wife were to ignore the cheating (I), then the husband would choose to cheat openly (O). However, if the husband chooses to cheat in secret (S), then the wife would choose to ignore the cheating (I). There is no pure-strategy Nash Equilibrium because if the wife chooses to catch her husband cheating (C), then the husband would choose to cheat in secret (S). It is important to note, as the article states, that the numbers in the payoff matrix above account for the “oppositional nature of the strategic relationship in the context of marital cheating.” After looking at the payoff matrix, I can see that there is no pure-strategy Nash Equilibrium, which in lecture was defined as a pair of strategies in which each player’s strategy is a best response to the other player’s strategy. Meanwhile, the wife (player 1) either ignores the cheating or catches him in the act, and her two pure strategies are I (ignore the infidelity) and C (catch him cheating). The husband (player 2) cheats openly or in secret thus, his two pure strategies are O (cheat openly) and S (cheat in secret). In this marital cheating game, the husband is cheating on his wife, while the wife remains faithful. According to the article, “between 30 and 60 percent of all married persons in the United States will engage in cheating at some point in their marriages.” Interestingly, the article states that men and women are equally likely to cheat on their spouse, and having an affair tends to have similar impacts on women and men. Some spouses pretend not to know and ignore it, while others search for ways to catch their significant other in the act. Unfortunately, marital cheating exists and occurs everywhere.
Catch a lover game wife how to#
How to catch a cheating spouse using game theory
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