Equilibrium with Mutual Altruism in the Pest Control Game

Equilibrium with an Altruistic Anil and a Self-Interested Bala

Strategic Decisions with Social Preferences

Consider a two-player game with the following material payoffs, where the first number in each pair is the payoff for Player A and the second is for Player B:

Assume Player A is entirely self-interested and seeks only to maximize their own material payoff. Player B, however, is altruistic and makes decisions to maximize the sum of both players' payoffs. Given these preferences, what is the most likely outcome of the game?

The Impact of Altruism on Strategic Outcomes

Two individuals, Player 1 and Player 2, must independently decide whether to make a 'Cooperative' choice or a 'Self-Interested' choice. A Cooperative choice benefits the other player at a small cost to oneself, while a Self-Interested choice benefits oneself at a larger cost to the other player. The final outcome depends on the combination of their personal preferences (how much they care about the other's payoff). Match each description of the players' preferences to the most likely strategic outcome.

In a two-player game where each player's payoff depends on the choices of both, a shift in Player A's preferences from pure self-interest to altruism will not change the optimal strategy for a purely self-interested Player B.

Analyzing Strategic Shifts Due to Altruism

Consider a scenario with two players, Alex and Ben, who must each choose between two actions: 'Cooperate' or 'Defect'. The material payoffs for each player depend on the combination of actions chosen. Alex is known to be purely self-interested, always choosing the action that maximizes their own material payoff. Ben is altruistic, meaning they care about both their own payoff and Alex's payoff.

Under what circumstances will Ben choose to 'Cooperate' even if 'Defect' would yield a higher personal material payoff for Ben?

Calculating the Altruism Threshold

Altering Strategic Outcomes

Two business partners, Sarah and Tom, must independently decide whether to pursue a 'High-Risk' or 'Low-Risk' venture. The table below shows the potential profits (in thousands of dollars) for each partner based on their combined choices. The first number in each cell is Sarah's profit, and the second is Tom's.

Initially, both partners are purely self-interested, aiming only to maximize their own individual profit. An analyst makes the following claim: 'If Sarah's preferences change so that she becomes altruistic (meaning she now also values Tom's profit in addition to her own), the final strategic outcome of their decision will not change.'

Evaluate the analyst's claim.

Degree of Altruism Determines Strategic Choice via Indifference Curve Shape