Three players (Cornelius, Oscar, and Reid) enter a game. Cornelius uses the cons

Question

Three players (Cornelius, Oscar, and Reid) enter a game. Cornelius uses the conservative approach to decision making, Oscar uses the optimistic approach, and Reid uses the minimax regret approach. The game is played as follows: each player chooses heads or tails, and the payoffs for each player are a function of the collective decisions of all three players. There are several possible outcomes: HHH, payoffs 2,-1,-1 TTT, payoffs -4, 3,1 HHT, payoffs -2, 2, 0 TTH, payoffs -2,0, 2 HTH, payoffs-1,-3, 4 THT, payoffs 0, 2, -2 THH, payoffs 3, -1, -2 HTT, payoffs 4, -2, -2 In these outcomes the players are ordered Cornelius, Oscar, Reid, and the

Explanation / Answer

(a) Cornelius uses the conservative approach. The possible payoffs for him playing H are (2, -2, -1, 4). The same for him playing T are (-4, -2, 0, 3). The worst possible payoff for choosing H is -2. The same for playing T is -4. So he would play H since his approach is conservative which means he wants to minimize his losses in the worst case.

Oscar uses the optimistic approach. For him, the best possible payoff for playing H is 2. The same for playing T is 3. So he would also play H since his approach is optimistic which means he wants to maximize his gains in the best case.

Reid uses the minimax regret approach. For him the maximum regret for playing H is 1-(-2)=3. The same for playing T is 6. As per minimax regret approach, he should minimize the maximum regret. So, he would choose H.

(b) I think the value of Lambda is missing here. Can you please check?

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