1
$\begingroup$

Suppose player 1 is a producer who can decide the quality of his production at the beginning of each period. So he has two strategies - Good, Bad. Player 2, the buyer decides at the beginning of each period how much to purchase, so she has 2 strategies - High, Low. Payoffs are realised after each period meaning buyer knows after the purchase if the quality was good or bad. I am struggling how to model this game and find SPE in finite ( say t=2) and infinite case. In finite case as in t=2, the producer will always choose Bad. But I am not sure how realising payoffs affects buyers decision in period 2. Does it affect at all since it is finite? Below is the payoff matrix.

[ \begin{array}{|c|c|c|} \hline \textbf{Producer (Player 1)} \backslash \textbf{Buyer (Player 2)} & \text{High} & \text{Low} \\ \hline \text{Good Tea (G)} & (2, 3) & (0, 2) \\ \hline \text{Bad Tea (B)} & (3, 0) & (1,1) \\ \hline \end{array} ]

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ That payoffs are realised after each period just means that both players observe the outcome of each period. In the finite case you can then solve the game by backwards induction. $\endgroup$ Commented May 19 at 8:23
  • 1
    $\begingroup$ Is this not a general rule in all repeated games where actions are always observed at the end of each period. They way this question highlighted this made me confused. Does this change anything? $\endgroup$ Commented May 19 at 23:21
  • 1
    $\begingroup$ Maybe it is just highlighted to exclude the possibility of a credence good. The assumption is standard, yes. $\endgroup$ Commented May 21 at 10:29

1 Answer 1

Reset to default
0
$\begingroup$

For the finite game, the last period game dominates. So for a finite game the last period will revery back to the stage game Nash Equilibrium of (B,L). Whether t = 2 or t = 50 in a finite game this will be true.

The infinite horizon case is different. Here we have a discount factor $\delta$ and "Grim Trigger" strategies. In this case let producer start with Good and buyer start with High. They will each continue this as long as the other player does not deviate.

If a player 1 deviates then the other player will punish the deviating player by playing Low. When we solve for the discount factor, we can look for a discount factor that yields a temporary punishment (that will revert back to cooperation), or a permanent punishment (that will not revert back to cooperation). $\delta \in (0,1)$ so if we solve for a $\delta \notin (0,1)$, then that specific temporary or permanent punishment cannot be supported as a strategy.

Here is a link to Munoz-Garcia's slides that show some examples. https://felixmunozgarcia.com/wp-content/uploads/2017/08/slides_131.pdf

Improve this answer
$\endgroup$

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.