Tuesday, September 9, 2014

Class #4 Highlights

In class #4, we studied the game theory value of an option. Unlike in finance, where an option's value accrues only to the extent that it is exercised, in game theory/outward thinking, the value of an option depends on its strategic effect, i.e. the degree to which it changes other players' moves. Success means that the option is not exercised since its whole point was to dissuade rivals from choosing moves that would trigger the option.

We saw this most clearly demonstrated in the NBA game. Absent the option, competition gave the bulk of the surplus created to the player, who enjoyed a 9 million dollar salary. By contrast, the presence of a right of first refusal option (often called a meet or buy or MFN option in other settings), effectively foreclosed competition. This allowed the incumbent team to capture the surplus.

The keys to this option were: (a) incumbent team offered the greatest surplus, and (b) some transaction cost frictions for any other team engaging in competition. If instead, the rival team and player produced $11 million in surplus, the restricted free agency clause would do nothing to curb competiition since the rival team could alway offer $10 million +$1 and foreclose the incumbent, albeit at considerable expense.

The second key highlight of the class was an analysis of WEGO games, i.e. games where moves are either simultaneous or sequential but unknown. In these games, one needs to guess the likelihood of various moves on the part of the rival. Rather than simply guessing moves, EMPATHY is needed to understand the rival's motives and, with this understanding, the implications for moves. A weak version of this idea is rationalizability. A move can be rationalized if their are some beliefs the rival might hold that make this move the best option. We can discard the possibility that the rival will choose moves that are not rationalizable.

In the prisoner's dilemma, rationalizability sufficed to predict the defect, defect outcome since cooperation is not a best response to any beliefs. In the Battle of the Sexes, however, rationalizability told up nothing since all moves are rationalizable.

A much stronger solution in WEGO games is Nash equilibrium, which says that beliefs are correct and both parties act on their beliefs. In the BoS game, coordination on either outcome is a Nash equilibrium. Non-coordination is not. Note that Nash equilibrium is appropriate when sophisticated or experience players participate in a game. Otherwise, more limited notions of sophistication better capture the situation.

In general, our technique for solving WEGO games is: Empathize then optimize, i.e. make predictions about rival beliefs (and the implied actions) and then choose your best action given this process.

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