Game theory and Insurance
The decision making process of whether to accept or reject life insurance proposals utilizes the concept of game theory we learned in class. Suppose player 1, P1, is the insurer, and player 2, P2, is a set of all the policy-holders. We can get a 2*2 payoff matrix of the insurer as illustrated below.
Among A, B, C, and D, C is the lowest as accepting a bad risk results in the largest loss. D>B as rejecting an ill proposer is better than accepting; A>B as accepting a healthy proposer is better than rejecting. In order to find the optimal strategy of the game for P1, one of the methods we could use is the minimax criterion, where we assume that P2’s unique goal is to harm P1 and deceive the insurers, thus reducing the payoffs. We can use the graph below to solve the problem. The vertical axis stands for the payoff to P1, and the horizontal axis is P2’s choice. Through a mixed strategy, we can get that P1 guarantees his payoff at v1 = (AD – BC) / (A+D-B-C), and P2’s optimal strategy is at Ph = (D-C)/(A+D-B-C).
The above model is rather naive and ideal because it doesn’t consider P1’s possibility to obtain other information such as the proposer’s health through asking the proposer to fill out medical information. This case is a more complicated case than the mixed strategies we learned in class where we assume players are seeking to maximize their expected payoff in mixed strategies. In this case, however, we assume that one of the player 2 is trying to lower the payoff of the other player through their decisions. In a real life scenario, this is possible but player 1 will rely on a lot more information they gather through their survey and experience as well.
https://www.casact.org/sites/default/files/database/astin_vol11no1_1.pdf