EWOT Four

On Thursday recitation, we played an Ultimatum Game in which we are supposed to make transaction with others. The players are in tune divided into proposers and responders. The proposers propose the way they want to distribute 10 scores and then the responder decides to accept or not. There’re 5 transactions, in which the proposers and responders are not allowed to communicate with each other. The people who get the highest score in the end is the winner.

The economic concept I got here is sort of theoretical. I tried to interpret the game in game theory.

What’s the best outcome for every player, or for the system, in that classroom? If everybody proposes a 5-5, in the end, every player will have a score of 25. Then everybody is the winner. But in reality, this is not going to happen because the obvious drawback of this game: the disclosure of other people’s decision.

For every player, to accept the transaction, no matter how much the other people propose, is the dominant strategy in this game. You may argue that if you reject a transaction in which the proposer get more than you do, your partner will get less and you’re more likely to win him. But, the question is, you both get less than others who made the transaction. This game is not a game between you and your partner. It’s a game between you and everybody in this classroom. It is not that make sure others get less than you, in most cases at your loss, that matters. It’s to get the highest score possible for YOU, that matters. You only have 5 chances to accumulate your score. If you accept while others accept, you maintain the gap between you and others. If you accept while others reject, you get advantage in this game. Thus, let’s assume people here are perfectly rational, although in reality there were 4 people who rejected a transaction, you can see from their number that they’re exceptions, every responder in this game, would accept any transaction. (10-0 situation is not a transaction at all since the obvious absence of exchange).

Keeping in mind that to accept is the dominant strategy, let’s think about why I said there’s a drawback within this game and who benefit from the drawback. As I suggested, the best outcome for the system is to get 25 for everybody. But we should notice that, since we’re not allowed to communicate with each other, we don’t know how the others will behave. As the second proposer, if you propose more than 5, or in other words, more than your partner had proposed, while others propose 5, you get advantage; if you do the same while others also propose more than 5, you maintain you position with others. Here, to propose more than the first proposer, for the second proposer, is the dominant strategy. As a result, in every 2-round transaction, the second proposer gets more than the first. Thus we can draw a conclusion: the second proposer of the two people benefit from the disclosure of other’s decision. This is where the unfairness comes from.

Based on the discussion above, we can easily find out the theoretically highest score possible in this game:

Let’s assume every player is perfectly rational.

Round：	Your Role：	How much to propose:	Accept&Reject:	Total  Gain
Round 1	Responder	5-5	Accept	5
Round 2	Proposer	9-1	Accept	14
Round 3	Responder	5-5	Accept	19
Round 4	Proposer	9-1	Accept	28
Round 5	Proposer/Responser	9-1/1-9	Accept	37/29

The situation mentioned above is an extreme situation. But it definitely helps us understand the game better. Here we see, the last round matters a lot in perfect situation. Your role in the last round determines who’s the winner.