Consider the following ‘war of attrition’. Two animals are in a stand off for a prey. They independently decide when to give up. Waiting is costly, but the animal giving up last wins the prey (they each get nothing if they walk away at the exact same time). Getting the prey gives a benefit of 80 while waiting costs 2 per unit of time. Formally payoffs are given as follows: u1(t1, t2) = ( −2t1 if t1 ≤ t2 80 − 2t2 if t1 > t2 u2(t1, t2) = ( 80 − 2t1 if t1 < t2 −2t2 if t1 ≥ t2, where ti is the amount of time animal i decided to wait. Assuming that animals aim to maximize payoffs (consciously or not), figure out the Nash equilibria of this game by answering the following questions (similar to how we proceeded to solve the Bertrand game). (a) Show that there is no Nash equilibrium where both animals wait a strictly positive amount of time. For this, consider two subcases: (i) both wait the same amount of time, or (ii) one gives in earlier than the other. (b) Assume now that one animal, say the first one, gives up right away (t1 = 0) while the other picks t2 ≥ 0. For which values of t2 do we have a Nash equilibrium? (c) Are the Nash equilibria identified in (b) Pareto efficent
Consider the following ‘war of attrition’. Two animals are in a stand off for a prey. They
independently decide when to give up. Waiting is costly, but the animal giving up last wins
the prey (they each get nothing if they walk away at the exact same time). Getting the prey
gives a benefit of 80 while waiting costs 2 per unit of time. Formally payoffs are given as
follows:
u1(t1, t2) =
(
−2t1 if t1 ≤ t2
80 − 2t2 if t1 > t2
u2(t1, t2) =
(
80 − 2t1 if t1 < t2
−2t2 if t1 ≥ t2,
where ti is the amount of time animal i decided to wait. Assuming that animals aim to
maximize payoffs (consciously or not), figure out the Nash equilibria of this game by answering
the following questions (similar to how we proceeded to solve the Bertrand game).
(a) Show that there is no Nash equilibrium where both animals wait a strictly positive
amount of time. For this, consider two subcases: (i) both wait the same amount of
time, or (ii) one gives in earlier than the other.
(b) Assume now that one animal, say the first one, gives up right away (t1 = 0) while the
other picks t2 ≥ 0. For which values of t2 do we have a Nash equilibrium?
(c) Are the Nash equilibria identified in (b) Pareto efficent?
The ideal conclusion of a game happens wherever there's no incentive to depart from the start strategy, in keeping with equilibrium, a notion in scientific theory. The equilibrium could be a notion in scientific theory that states that the simplest outcome of a game is one within which no player has associate incentive to depart from their elite strategy when evaluating the strategy of associate opponent.
Overall, dynamic actions can offer no progressive profit to a private providing that alternative players' ways stay unchanged. There may well be many author equilibria in a very game, or none in any respect.
- The equilibrium could be a scientific theory decision-making theorem that argues that if a player sticks to their beginning strategy, they'll attain the required result.
- When considering the selections of alternative players, every player's strategy is perfect within the equilibrium. each player wins as a result of all of them bring home the bacon the result they require.
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