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opendigital / RL-collective-action

In this repo we save all information about our research related to reinforcement learning for collective action games!
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Calculate Nash Equilibrium of Game #2

Open shatayu opened 3 years ago

shatayu commented 3 years ago

E := the total amount everyone contributes over 20 rounds i := the total amount you contribute over 20 rounds

cooperating amount: 1.6 (E + i) / 4 = 0.4(E + i) competing amount: 25 20 - i

0.4(E + i) + 500 - i 500 - 0.6i + 0.4E

compute the best value of i for every single value of E

The nuance: E and i are dependent variables. In each round, the player's contribution may influence the other players to contribute more in the next round. Figure out the Nash equilibrium given this probability distribution and/or make assumptions about this probability distribution.

Also: maybe express the Nash equilibrium as the sum of round actions?

sbrunswi commented 3 years ago

@shatayu!

here is an easy link to learn how to calculate the nash: https://www.economics.utoronto.ca/osborne/2x3/tutorial/NEFEX.HTM#:~:text=To%20find%20the%20Nash%20equilibria,each%20action%20profile%20in%20turn.&text=Neither%20player%20can%20increase%20her,profile%20is%20a%20Nash%20equilibrium.&text=By%20choosing%20A%20rather%20than,0%2C%20given%20player%202's%20action.