# 9

TL;DR = write a python script to win this applied game theory contest for \$1000. Based on Prisoner's Dilemma / Tragedy of the Commons but with a few twists. Deadline Sunday August 18.

https://brilliant.org/competitions/hunger-games/rules/

I. Food and Winning

Each player begins the game with 300(P−1) units of food, where P is the number of players.

If after any round you have zero food, you will die and no longer be allowed to compete. All players who survive until the end of the game will receive the survivor's prize.

The game can end in two ways. After a large number of rounds, there will be a small chance each additional round that the game ends. Alternatively, if there is only one person left with food then the game ends. In each case, the winner is the person who has the most food when the game ends.

II. Hunts

Each round is divided into hunts. A hunt is a game played between you and one other player. Each round you will have the opportunity to hunt with every other remaining player, so you will have P−1 hunts per round, where P is the number of remaining players.

The choices are H = hunt (cooperate) and S = slack (defect), and they use confusing wording here, but as far as I can tell the payoff matrix is (in units of food)

 H / C S / D H / C 0:0 -3:1 S / D 1:-3 -2:-2

What's interesting is you don't get the entirety of your partner's history (so strategies like Tit-Tit-Tit for Tat don't work) instead you get only their reputation, which is the fraction of times they've hunted.

To further complicate the Nash equilibria, there's the option to overhunt: a random number m, 0 < m < P(P−1) is chosen before each round (round consisting of P−1 hunts, remember) and if the total number of hunt-choices is at least m, then each player is awarded 2(P−1) food units (2 per hunt).

Your python program has to decide at the start of each round whether or not to hunt with each opponent, based on:

• the round number