BIO150Y: Evolution of Cooperation  Reference 
Frequently Asked Questions
Expanded treatment of some of the tutorial concepts
How is my payoff matrix built? In our prison example, each player has two possible moves (options): cooperate (with your partner) and remain silent or defect (betray your partner) and implicate your partner in the major crime. Since your fate depends both on your move and your partner's move, there are in fact four possible outcomes with different prison terms (payoffs):
The outcomes can be summarised in a 2x2 payoff matrix as shown below.
How is the costbenefit payoff matrix built? In the chimpanzee mutual grooming example, each chimp has two options: cooperate and groom the other chimp, or defect and refuse to reciprocate. It is assumed that it costs 2 points to groom a partner, and the benefit of being groomed is 4 points. There are four outcomes:
The outcomes can be summarised in a 2x2 payoff matrix as shown below.
To simplify its use, the (raw) costbenefit payoff matrix can be adjusted so that the lowest payoff is zero rather than negative. In this example, we can add 2 points to each cell so that the resulting (normalized) costbenefit payoff matrix looks like this:
Some common strategies in the Prisoner's Dilemma Game ALTERNATE: The player alternates between C and D, starting with a C. ALWAYS COOPERATE: The player always plays C, no matter what their partner has played in the past. Also known as sucker. ALWAYS DEFECT: The player always plays D. Also known as cheat. GRUDGER: The player starts playing C and continues to do so until the other player plays D. After that it plays D for the rest of the game with that particular partner. RANDOM: The player chooses either C or D with equal probability. SNEAKER: The player starts with a C and then plays whatever its partner play in the previous move. However, at random intervals it plays D. TIT FOR TAT: The player starts playing C and then plays whatever its partner did in the previous move. TIT FOR TWO TATS: The player plays C in the first and second moves. After that, if its partner played D in the two previous moves they play D, otherwise they continue to play C. TWO TITS FOR TAT: The player starts with C, and then if its partner plays D, then plays D in the following two moves, otherwise plays C.
Calculating relative success In an imaginary evolutionary game, 24 players pair at random and play a multiplemoves game. Points are then totalled for all players in each strategy. In this example, the 12 suckers amass only 240 points compared to the 840 points amassed by the 12 cheats. The relative success of each strategy is expressed as a proportion of the total points amassed; for suckers this is a relative success of 0.22, which is 240 points divided by the total points of 1080. The number of players for each strategy in the next round of games (generation) is simply the relative success of the strategy multiplied by the total number of players in the population (24). Note that this assumes that population size stays constant and just the proportion of players in each strategy changes. The new player numbers are rounded to the nearest integer. So in the next generation of the game, there will be 5 suckers and 19 cheats.

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