Peter Norvig on Nash Equilibrium - Dictionary of Arguments
Norvig I 669
Nash Equilibrium/Norvig/Russell: every game has at least one equilibrium.(Cf. >Prisoner’s dilemma) Clearly, a dominant strategy equilibrium is a Nash equilibrium (…) but some games have Nash equilibria but no dominant strategies.
Problem: The dilemma in the prisoner’s dilemma is that the equilibrium outcome is worse for both players than the outcome they would get if they both refused to testify. In other words, (testify, testify) is Pareto dominated by the (-1, -1) outcome of (refuse, refuse). Is there any way for Alice and Bob to arrive at the (-1, -1) outcome?
Solutions: we could change to a repeated game in which the players know that they will meet again. Or the agents might have moral beliefs that encourage cooperation and fairness. That means they have a different utility function, necessitating a different payoff matrix, making it a different game. >Value/AI research.
Norvig I 687
In 1950, at the age of 21, John Nash published his ideas concerning equilibria in general (non-zero-sum) games. His definition of an equilibrium solution, although originating in the work of Cournot (1838)(1), became known as Nash equilibrium. After a long delay because of the schizophrenia he suffered from 1959 onward, Nash was awarded the Nobel Memorial Prize in Economics (along with Reinhart Selten and John Harsanyi) in 1994. The Bayes–Nash equilibrium is described by Harsanyi (1967)(2) and discussed by Kadane and Larkey (1982)(3). Some issues in the use of game theory for agent control are covered by Binmore (1982)(4). >Game theory/AI Research, >Prisoner`s dilemma.
1. Cournot, A. (Ed.). (1838). Recherches sur les principes mathématiques de la théorie des richesses.
L. Hachette, Paris.
2. Harsanyi, J. (1967). Games with incomplete information played by Bayesian players. Management
Science, 14, 159-182.
3. Kadane, J. B. and Larkey, P. D. (1982). Subjective probability and the theory of games. Management
Science, 28(2), 113-120.
4. Binmore, K. (1982). Essays on Foundations of Game Theory. Pitman._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Stuart J. Russell
Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010