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Numerical solutions for equilibria in a game with a safety-performance tradeoff

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nicholaskemery/ai_incentives2

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The code in this repository is meant to find Nash equilibria for the following model:

We assume that n players produce safety, s , and performance, p , as s i = A i K s , i α i p i θ i , p i = B i K p , i β i . for i = 1 , , n . The K are inputs chosen by the players, and all other variables are fixed parameters.

In a Nash equilibrium, each player i chooses K s , i and K p , i to maximize the payoff π i := ( j = 1 n s j 1 + s j ) ρ i ( p ) ( 1 j = 1 n s j 1 + s j ) d i r i ( K i , s + K i , p ) , subject to the other players' choices of K s and K p . Here ρ i ( p ) is a contest success function (the expected payoff for player i given a safe outcome and a vector of performances p ), and d i is the damage incurred by player i in the event of an unsafe outcome.

The easiest way to use this code is via the API in scenarios.py: just run python3 scenarios.py from this directory to run some example scenarios, or import the Scenario class and run your own scenarios.

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