Animal Behavior Zool 5312 - Graduate Student Project

Animal Behavior Zool 4312 – Life is a game All (or nearly all) behavior is a game. That is, individuals choose behavioral strategies whose payoff depends on the strategies (and their frequencies) played by other individuals with whom they interact. The object of this assignment is to prompt you to see life for the game that it is and think about the logic of Game Theory.

For the following examples, find the ESS – remember there can be (1) a single pure strategy ESS, (2) multiple pure strategy ESSes (but only one ESS is present at any time), or (3) a multi-strategy ESS, where p=frequency of playing strategy ‘x’ and (1-p) = frequency of playing strategy ‘y’, where p can be calculated based on the payoff values (see your class notes).

I want you to play some following games, determine the ESS(es) as above, and calculate the frequency of the strategies if the ESS is a multi-strategy ESS. But first,

(1) Fill in the following three matrices with numerical values to illustrate, respectively (i.e., from left to right) (1) B is a single strategy ESS, (2) the ESS is a mixture of A & B, (3) multiple ESSes.

A B A B A B

(2) Advertisement Game – Male birds sing on Texas Tech campus to advertise themselves to females. While all males may apparently advertise by singing, not advertising yourself may still seem like a candidate strategy (albeit not a good one) to attract mates. So “advertise” and “not advertise” define the 2 discrete strategies

Assembled a payoff matrix under the following assumptions (the actual numbers are not as important as the relative ranking – my advice is keep it simple): (1) If both males should advertise OR both male do not advertise, they have an equal chance of finding mates. So ask yourself, which cells (two of them) of the matrix is this referring to? Then place a number in them that is consistent to the information I gave you. (2) Advertising has a cost, whereas not advertising does not cost you anything. Ask yourself again, what cells is this referring to? You now have more information, so you may need to modify your value(s) from part one. (3) Advertising while your opponent doesn’t greatly increases your relative payoff (beyond the cost of advertising), whereas the opposite greatly decreases your payoff.

A. From this information fill in the matrix with numbers (which I feel is easier) or variables (harder), but they must conform to the stated assumptions given above). B. Determine the ESS. C. Interpret the result - what does the payoff matrix and the ESS tell you about advertising, individual fitness, and mean fitness? In other words, would everyone be better off (higher mean payoff) if they all advertise or all do not? Yes or no – and explain why.