Consider the following game:

Player B

Accept Reject

Accept 5, 6 13, 3

Player A Reject 7, 5 8, 4

What is the maximum A is willing to offer to B if it plays Reject?

(Note: if it must be less than 10, enter 10)

Question

Consider the following game:

Player B

Accept      Reject

Accept     5, 6          13, 3

Player A     Reject       7, 5          8,  4

What is the maximum A is willing to offer to B if it plays Reject?

(Note: if it must be less than 10, enter 10)

BlackTom AI · Accepted Answer

The question presents a 2x2 payoff matrix for a two-player game and asks: what is the maximum amount A is willing to offer to B if A chooses the Reject option?

First, identify the subgame that follows A choosing Reject. If A rejects, B then chooses between two outcomes: 
- B Accept leads to the cell (A, B) = (7, 5) 
- B Reject leads to the cell (A, B) = (8, 4) 
So, in this subgame without any transfer, B would prefer the Accept option, since 5 > 4.

Now consider what it would mean for A to offer something to B in order to influence B’s decision. Any offer N from A to B would increase B’s payoff in the (Reject, Accept) outcome from 5 to 5 + N, while reducing A’s payoff in that same outcome from 7 to 7 − N. B will accept as long as their payoff in Accept is at least as good as their payoff if they reject. Since B’s rejection payoff is 4, and the Accept payoff is already 5 (which is greater than 4), B is already better off accepting even with no offer (N = 0).

Because B already prefers Accept when A rejects, A has no incentive to give B any positive amount: giving any amount would only decrease A’s own payoff (since A’s payoff would drop from 7 to 7 − N, while B’s payoff would increase). Therefore, the maximum amount A would be willing to offer to B is 0.

A quick cross-check: if A offered any positive amount N > 0, A’s payoff in the Reject-Accept branch would become 7 − N, which is less than 7, and since B’s decision remains Accept (because 5 + N > 4), A would be worse off. Hence the optimal (for A) transfer is zero.

Note: If the problem instruction about entering 10 for values less than 10 were relevant, it would be an instruction for how to handle a constraint, but here the logical maximum A would offer is 0, given B’s baseline preference for Accept without any transfer.

COMM_V 295 105 106 2025W1 Participation/Math Quiz #2

Consider the following game: Player B Accept Reject Accept 5, 6 13, 3 Player A Reject 7, 5 8, 4 What is the maximum A is willing to offer to B if it plays Reject? (Note: if it must be less than 10, enter 10)

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