[passion]

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Well first, I wonder if there is a "right" answer to this question because "optimal strategy" would essentially be relative to each player's idea of what is and is not a good deal.

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The optimal straties in game theoretic context reffered to as a Nash Equillibrium (NE). A NE is a set of strategies such that player A is reacting optimally (i.e getting the highest payoff) given Bs strategy and player B is reacting optimally given As strategy -i.e. both players are acting optimally given the strategies of the other player. Using this concept of an equillibrium in a finite period game what is fair or what is a good deal doesn not matter.

As was pointed out above there may be reasons to expect typical players to deviate from NE strategies in this sort of game (in the real world).

Passion