benelliott

In Freaky Fairness the author discusses the problem of multi-player game theory problems where all players have access to each-other's source code. He gives an algorithm called Freaky Fairness, and makes the claim that 'all players run Freaky Fairness' is both a Strong Nash Equilibrium and a Pareto Optimum. Unfortunately, as far as I can tell, this claim is false. For reference, the algorithm of Freaky Fairness works as follows: 1. Calculate the security values in mixed strategies for all subsets of players. 2. Divide all other players into two groups: those whose source code is an exact copy of Freaky Fairness (friends), and everyone else (enemies). 3. If there are no enemies: build a Shapley value from the computed security values of coalitions; play my part in the outcome that yields the highest total sum in the game; give up some of the result to others so that the resulting allocation agrees with the Shapley value. 4. If there are enemies: play my part in the outcome that brings the total payoff of the coalition of all enemies down to their security value. Now consider the following simple game for three players: 1. Each player chooses one player to nominate. 2. They can nominate themselves but they don't have to. 3. If a player gets nominated by at least two players (possibly including themselves) then they win the game and receive $300 4. If every player gets nominated exactly once then nobody gets anything. Conventional competitive game theory notes that each player has a dominant strategy of nominating themselves, and so nobody gets anything. Since the game potentially offers an $300 prize there is room for improvement here. Lets see how Freaky Fairness does: * The empty coalition and all coalitions with only one player have a security value of 0. * All coalitions with at least two players have a security value of $300 (this is independent of whether you use the alpha method, the beta method or mixed strategies to calculate security valu