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URS '23, urban data, and computer science. A student at Cornell university pursuing a bachelor degree in Urban and Regional Studies (URS).
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18 October 2022Social Evolution
by Yucheng Zhang
Continues last lecture’s discussion on social evolution game.
Every player is a subset of strategies. We are interested if in the society of P and Q, the dominating group P is immune of the occurrence of a small population of Q. Recall that the definition of immunity is that P is immune against Q if Payoff (P,P) > Payoff (P, Q) or Payoff (P,P) = Payoff (P,Q) and Payoff (P,Q) > Payoff (Q,Q).
Evolutionary Stable Strategy (ESS) is a strategy in an evolutionary game that is immune to all other sets of strategy.
Consider an alternative game to the Hawk and Dove game that has a creator between Hawk and Dove. Hawk is aggressive, while the Dove is passive
| Strategy | H | M | D |
|---|---|---|---|
| H | 0,0 | 3,1 | 6,2 |
| M | 1,3 | 3,3 | 5,3 |
| D | 2,6 | 3,5 | 4,4 |
How to find a evolutionary stable strategy? H is not ESS because it is not immune to M, (H,H)<(H,M) Doves is not immune to Hawks M is immune against Hawk using the second comparison rule: Consider a society dominated by M with the introduction of H, (M,M) = (M,H), and (M,H)>(H,H), thus immune. M is immune to D because (M,M)>(M,D)
*Concentrate on the diagonals and check if it is nash.
In traditional Hawk and Dove games, the ESS only exists under mixed strategy.
| A | H | D |
|---|---|---|
| H | -1,-1 | 4,0 |
| D | 0,4 | 2,2 |
Evolutionary Neutral Strategy: The population does not get wiped out more than the dominating strategy.
Update Oct 20th, continued discussion on ESS and ENS.
In a evolutionary society you do not choose a strategy, you are the strategy.
Consider the traveller’s dilemma, where a society is dominated by 2s. Any introduced population with a value different
than 2, for example 48, will constantly get a payoff of 0, thus 2s is the Evolutionary Stable Strategy that is immune
from any other population/strategy.
Extensive-form Game
An extensive-form game is a game that has a clear sequence of “who moves when”, aka some sequence of order. There are four kinds of EFG:
- perfect information, which is consist of the following 4 elements
- Players
- Nodes
- Initial node (the start of the game)
- Terminal nodes (the payoffs of the game)
- Decision nodes (The time points that players should choice)
- Actions/branches (strategies of the game, which could be write down to another player to play the same as you would)
- Payoffs
Example: 
- imperfect information game
at some time player(s) has to make a move without knowing the current progress. The nodes are often marked by breaking lines.
Example: 
Notice that the dashed lines with 2, meaning that the player have to choose between L and R without knowing another
player’s choice between T and B.