Degree of Altruism Determines Strategic Choice via Indifference Curve Shape
The degree to which a player is altruistic directly influences their strategic choices in a game. This causal link operates through the shape of their indifference curves: a lower level of altruism results in steeper curves, which can lead the player to prefer a different, potentially less cooperative, outcome than they would with a higher degree of altruism.
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CORE Econ
Ch.4 Strategic interactions and social dilemmas - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
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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:
Player B: Strategy X Player B: Strategy Y Player A: Strategy X (3, 3) (1, 4) Player A: Strategy Y (4, 1) (2, 2) 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.
Tom: High-Risk Tom: Low-Risk Sarah: High-Risk (10, 10) (0, 12) Sarah: Low-Risk (12, 0) (5, 5) 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
Learn After
Two individuals, Jamie and Chris, must decide how to divide a resource. Imagine a graph where Jamie's share is on the vertical axis and Chris's share is on the horizontal axis. A straight, downward-sloping 'Allocation Line' shows all possible divisions.
- Jamie's indifference curves are solid and relatively flat, meaning Jamie is willing to give up a small amount of their own share to see Chris's share increase by one unit.
- Chris's indifference curves are dashed and relatively steep, meaning Chris must be given a large increase in their own share to be willing to give up even one unit of their share.
Based on this information, which statement provides the most accurate analysis of their preferences and likely choices?
Analyzing Preferences in a Resource Allocation Scenario
Impact of Altruism on Allocation Choices
Altruism, Indifference Curves, and Strategic Choice
An individual's preferences about their own payoff versus another person's payoff can be represented by indifference curves. On a graph where the individual's own payoff is on the vertical axis and the other person's payoff is on the horizontal axis, match each type of preference to the shape of the indifference curve that represents it.
Consider two individuals, Player A and Player B, whose preferences for allocating a sum of money between themselves are represented by indifference curves. On a graph where a player's own payoff is on the vertical axis and the other player's payoff is on the horizontal axis, Player A's indifference curves are significantly steeper than Player B's. This implies that if both players were offered an identical choice between keeping the entire sum for themselves or splitting it evenly, Player A would be more likely than Player B to choose the even split.
Predicting Strategic Shifts from Changes in Altruism
Evaluating a Policy to Foster Cooperation
Analyzing a Shift in Allocation Strategy
An individual is deciding how to allocate a fixed sum of money between themself and another person. Their preferences are represented by a set of indifference curves on a graph, where their own payoff is on the vertical axis and the other person's payoff is on the horizontal axis. The possible allocations are shown by a straight, downward-sloping line. Initially, the individual chooses an allocation that gives a significant portion to the other person. If this individual's feeling of goodwill towards the other person decreases significantly, what is the most likely consequence for their indifference curves and their chosen allocation?