Person A can trust or not trust person B. If person A decides to not trust, both players get a zero payoff. If Person A trusts, Person B can abuse or honour the trust bestowed upon them. If person B abuses Person A's trust, Person A gets a negative payoff. If person B honours person A's trust, person A gets a positive payoff. Person B can be of two types: trustworthy or not trustworthy. Both trustworthy and untrustworthy person B types get a positive payoff if they honour A's trust. But a trustworthy person B prefers to honour person A's trust whereas an untrustworthy B prefers to abuse. Nature determines randomly if person B is trustworthy or not. Person B knows if they are trustworthy or not but person A doesn't know. The probability that person B is not trustworthy is a and the probability that person B is trustworthy is 1 a. a is common knowledge, meaning that both person A and person B know the probability of person B being (not) trustworthy. a) Draw the extensive game version (i.e. in game tree format). Assign payoffs for each strategy combinations, justifying your selection of payoffs. b) Draw the strategic game version (i.e. in matrix format) of the game assuming a= 0.5 (the probability that person B is not trustworthy is 0.5). That is, determine which strategies are available to each player; calculate expected payoffs for each combination of strategies with a = 0.5; and enter those payoffs in the matrix of conditional strategies. Find the pure strategy Nash equilibria of this game with incomplete information, assuming a = 0.5. c) Draw the strategic game version (i.e. in matrix format) of the game assuming a 0.8 (the probability that person B is not trustworthy is 0.8). That is, determine which strategies are available to each player; calculate expected payoffs for each combination of strategies with a = 0.8: and enter those pavoffs in the matrix of conditional strategies, Find the pure
Person A can trust or not trust person B. If person A decides to not trust, both players get a zero payoff. If Person A trusts, Person B can abuse or honour the trust bestowed upon them. If person B abuses Person A's trust, Person A gets a negative payoff. If person B honours person A's trust, person A gets a positive payoff. Person B can be of two types: trustworthy or not trustworthy. Both trustworthy and untrustworthy person B types get a positive payoff if they honour A's trust. But a trustworthy person B prefers to honour person A's trust whereas an untrustworthy B prefers to abuse. Nature determines randomly if person B is trustworthy or not. Person B knows if they are trustworthy or not but person A doesn't know. The probability that person B is not trustworthy is a and the probability that person B is trustworthy is 1 a. a is common knowledge, meaning that both person A and person B know the probability of person B being (not) trustworthy. a) Draw the extensive game version (i.e. in game tree format). Assign payoffs for each strategy combinations, justifying your selection of payoffs. b) Draw the strategic game version (i.e. in matrix format) of the game assuming a= 0.5 (the probability that person B is not trustworthy is 0.5). That is, determine which strategies are available to each player; calculate expected payoffs for each combination of strategies with a = 0.5; and enter those payoffs in the matrix of conditional strategies. Find the pure strategy Nash equilibria of this game with incomplete information, assuming a = 0.5. c) Draw the strategic game version (i.e. in matrix format) of the game assuming a 0.8 (the probability that person B is not trustworthy is 0.8). That is, determine which strategies are available to each player; calculate expected payoffs for each combination of strategies with a = 0.8: and enter those pavoffs in the matrix of conditional strategies, Find the pure
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.5P
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Transcribed Image Text:Person A can trust or not trust person B. If person A decides to not trust, both players get a zero payoff. If
Person A trusts, Person B can abuse or honour the trust bestowed upon them. If person B abuses Person A's trust, Person A
gets a negative payoff. If person B honours person A's trust, person A gets a positive payoff. Person B can be of two types:
trustworthy or not trustworthy. Both trustworthy and untrustworthy person B types get a positive payoff if they honour
A's trust. But a trustworthy person B prefers to honour person A's trust whereas an untrustworthy B prefers to abuse.
2
Nature determines randomly if person B is trustworthy or not. Person B knows if they are trustworthy or not but person A
doesn't know. The probability that person B is not trustworthy is a and the probability that person B is trustworthy is 1 a.
a is common knowledge, meaning that both person A and person B know the probability of person B being (not) trustworthy.
a) Draw the extensive game version (i.e. in game tree format). Assign payoffs for each strategy combinations, justifying
your selection of payoffs.
b) Draw the strategic game version (i.e. in matrix format) of the game assuming a = 0.5 (the probability that person B is not
trustworthy is 0.5). That is, determine which strategies are available to each player; calculate expected payoffs for each
combination of strategies with a = 0.5; and enter those payoffs in the matrix of conditional strategies. Find the pure
strategy Nash equilibria of this game with incomplete information, assuming a = 0.5.
c) Draw the strategic game version (i.e. in matrix format) of the game assuming a=0.8 (the probability that person B is not
trustworthy is 0.8). That is, determine which strategies are available to each player; calculate expected payoffs for each
combination of strategies with a = 0.8; and enter those payoffs in the matrix of conditional strategies. Find the pure
strategy Nash equilibria of this game with incomplete information, assuming a = 0.8.
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