Abstract
Some finite and symmetric two-player games have no (pure or mixed) symmetric Nash equilibrium when played by partly morally motivated players.The reason is that the “right thing to do” may be not to randomize. We analyze this issue both under complete information between equally moral players and under incomplete information between players of arbitrary degrees of morality. We provide necessary and sufficient conditions for the existence of equilibrium and illustrate the results with examples and counter examples.
Highlights
In economics and non-cooperative game theory, economic agents and players are usually assumed to be pure consequentialists, that is, to evaluate their alternative courses of action exclusively in terms of the consequence for themselves and perhaps for others
Some finite and symmetric two-player games have no symmetric Nash equilibrium when played by partly morally motivated players.The reason is that the “right thing to do” may be not to randomize
We provide necessary and sufficient conditions for the existence of equilibrium and illustrate the results with examples and counter examples
Summary
In economics and non-cooperative game theory, economic agents and players are usually assumed to be pure consequentialists, that is, to evaluate their alternative courses of action (consumption or production plans, strategies) exclusively in terms of the consequence for themselves and perhaps for others. People may to some extent be driven by deontological motivations, such as a wish to “do the right thing” in the given situation Such a participant in a public goods game may, for example, contribute the amount that would maximize the group’s welfare if everybody would do likewise, in line with Immanuel Kant’s (1785) categorical imperative, to “act only on the maxim that you would at the same time will to be a universal law.”. A Kantian moralist may instead use the second pure strategy. This will result in material payoff zero to both, but the moralist may obtain psychological utility from behaving in a way he/she wishes all would in such interactions. Theorem 1 and Proposition 6 together establish necessary and sufficient conditions for the existence of symmetric Nash equilibrium between partly morally motivated players under incomplete information about others’ degree of morality
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