Game Theory has proven no such thing.
Firstly, Game Theory does not assert morality is analogous to rational action or decision-making. Rationality does not assume a moral force or stance - it merely compels the agent to pursue their desires, as efficiently and maximally as possible. Morality within a game is justified only if a moral strategy is maximally beneficial. Thus within a game evil incarnate as strategy, is equally as valid as morality if the payoff is maximally beneficial to the player so bedevilled, or enlightened.
Also the theory assumes rational interactions between rational agents, under ideal circumstances ? it?s a model. The theory is underpinned by rational agency ? all players are rational and therefore will pursue their desires as efficiently and maximally as possible. The rational agent is assumed to be without race, class and gender ? disembodied, without character, and driven by self-interest ? seeking only maximum utility (greatest benefit to themselves).
Generally, it is thought that a moral stance will cause an agent to sacrifice their personal interests or aims. Prima facie, morality appears to run counter to rationality. However in ?Morals by Agreement (1986) Gauthier, using Game Theory, argues that our conceptions of rationality are misconceived. The aim of rationality ? to maximise self-interest ? does not in itself direct how this should be done. A direct quote from the posted link follows:
?In terms of the utility-maximizing conception of rationality which he has accepted until recently (Gauthier, forthcoming), Gauthier argues that the aim of maximizing utility does not mean that we should, at each decision point, maximize utility. Instead we should reason in ways which are utility maximizing.?
Game Theory applied to Ethics is still an emerging discipline. It has many detractors and many of its underlying tenets are challenged ie ?the rational agent.? However, Game Theory does provide a fascinating insight into strategic thinking under ideal conditions.
http://plato.stanford.edu/entries/game-ethics/ Interestingly, Game Theory is taught extensively in business schools throughout the world as it forms part of economic and market curricula. I recent study found 56% of MBAs (business school graduates) admitted to cheating within the previous year. Reasons given were that they thought others were doing it. Game Theory in action it would seem.
http://www.philly.com/mld/inquirer/news/local/15551798.htm