Game Theory

I have recently been studying Game Theory but only superficially (see Game Theory and the Humanities (Brams) and Super Cooperators (Nowak, a brilliant book). My son, David is studying the real thing at the moment at university. Recently, he sent me the lecture slides for his opening lectures.

What is interesting is that Game Theory is all about human interactive behaviour to which mathematical modelling is applied or, as David's notes tell us:

'Game theory is a mathematical method for analysing strategic interaction.' Nobel Prize Citation, 1994

'Briefly put, game and economic theory are concerned with the interactive behaviour of Homo rationalisâ??rational man.'  Robert J. Aumann, 1985

'Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. Game theory provides general mathematical techniques for analyzing situations in which two or more individuals make decisions that will influence one another's welfare.' Roger B. Myerson, 1991

'A game is being played whenever people have anything to do with each other.' Ken Binmore, 2007

A well recognised application is the Prisoner's Dilemma, or The Gain Game, on Core's training courses!

In the classic model, there are 4 choices: in 1) and 2) each prisoner seeks to 'win' it all at the expense of the other; 3) both 'defect' and have a less costly than losing outcome, or 4) both cooperate (implicitly at least) and maximise the joint outcome, less satisfactory than winning at the expense of the other but preferable to losing in 1) or 2) or the result for each in 3).


4) A and B cooperate to maximise joint outcome 2) B wins, A loses
1) A wins, B loses 3) A defects, B defects, costly to both though less costly than losing in a loss/win

I may not have explained that well. However, it occurs to me that this is broadly what happens in some negotiations we see in mediations. Both parties wish to achieve a 'win': 1) or 2). That is not (usually) available in negotiation or mediation. 3) possibly represents a delayed, door of the court, more costly, more arms length settlement. 1) represents a prudent commercial arrangement reached only by communicating in the process of mediation. Neither party is satisfied in the sense of achieving a maximal result; but each saves more than it will lose on a cost/benefit analysis, unless it were ultimately to win in court - and, even then.......