Advanced Game Theory, Golden Balls Edition

My Twitter feed is, quite rightly, full of links to this remarkable episode of Golden Balls, the British game show that puts contestants in a classic game theory dilemma of “splitting or stealing” the grand prize:

If you have time for more, here’s another famous episode, with a very different display of strategy and tactics:

3 thoughts on “Advanced Game Theory, Golden Balls Edition”

  1. In the classic one-round prisoner’s dilemma situation, the primary game payoff constitutes the complete game outcome, leading to the dominating response (“Steal” in this game’s parlance) that is optimal regardless of opponent action…you can do no worse by taking it.

    Here, beyond the gamesmanship, there are exogenous components to value: Individual’s value on self-perception/peer perception after taking an action. For example, if an opponent will definitely steal, an individual will always receive no money, but different individuals might put different values on also stealing themselves (and risking having others laugh at them for being greedy and nobody getting any money) and splitting (and being a sucker…or a good person taken advantage of). This could lead to the lack of a dominant outcome…I want to split if they split, but steal if they steal, for example, similar to Tit-for-Tat in repeated Prisoner’s Dilemma tournaments.

    “Stealing” may get more likely as the stakes rise, but the question is whether this is really greed: The incremental payoff only occurs if an opponent chooses “Split”, and in that situation the payoff is an incremental utility for twice as much money compared to a significant amount of money (not necessarily a huge incremental utility for found money) versus cost of negative perceptions; there are probably a reasonable number of “good” people out there who prefer the “fair” option. However, it is clear that human nature is to try to punish someone greedy and not let them get away with stealing by benefiting (numerous tests where one party splits a pot between the players and the other accepts or rejects the split demonstrate this)… So I wonder whether many people steal when stakes get high, not because of the potential for gain, but because they think that the other person is more likely to steal and they don’t want to let them get away with it.

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