3. Steal or Split! 000 QR). If both choose split, then the prize is divided even

Question

3. Steal or Split! 000 QR). If both choose split, then the prize is divided evenly (50-50). If one chooses split and the other steal, the person who steals gets the entire prize. If both choose steal, however, then both walk away with nothing. You are one of the participant! You have no indication on whether or not you can trust the other participant. What will be your best strategy (what are you going to do (steal or split) and why?) Scenario 1: You are not allowed to communicate with the other participant Each of two participants independently chooses to split or steal the final prize (say 100 Scenario 2: You are allowed to communicate with the other participant What if the game (scenario 2) is repeated many times, will this help you or not to find a better strategy or not? Justify

Explanation / Answer

The game involves what is known as “Split or Steal” in which two participants make the decision to “split” or “steal” to determine how the final jackpot is divided.

The participants play for 100000 QR. They will also have the opportunity to negotiate with each other before making their decisions or as asked in first scenario they will not communicate. In most cases, both participants will try to convince each other to split as it is the most mutually beneficial strategy. However, this split-spit strategy, while maximising welfare, is not a stable strategy. Most games end up in either one or both parties defecting. In the former, one party goes home with all the money (and leaving the other with nothing). Or in the latter, which happens more often, both parties loses all the money and goes home empty-handed. Very rarely will both players end up in a split-split scenario.

To understand this, we can draw up a payoff matrix as such:

However, in this game, as long as one player chooses to steal, neither player has a better strategy. That is to say, all three strategies that involve stealing are Nash equilibria (as shown by the shaded cells) and (Split, Split) is an unstable strategy.

However, the game is not as simple as that. There were many facets to strategy that involved deeper psychological implications. To model this, we cannot assume that the payoff is solely based on the money each player gets to win. Let’s instead add the additional factor, S, to represent the disutility derived from losing as a result of being swindled by the other player.

Now both players have a dominant strategy of (Steal, Steal). However, this is not ideal to both parties. To counter this, Player 1 insisted that he will steal regardless of what Player 2 does. Assuming Player 1’s claim is true, the game is now reduced to Player 2 deciding between Split or Steal, in which Player 1 should choose to Steal as to avoid a negative payoff (i.e. to get 0 rather than -S).

To further encourage a (Split, Split) outcome, Player 1 then assures Player 2 that if he splits and Player 1 wins the entire pot, Player 1 will then give Player 2 half of the prize money. Player 2 is naturally suspicious of this claim, as Player 1 could very well keep the winnings to himself. We can represent this suspicion with a new variable, H, which denotes the probability (between 0 and 1) of Player 1 being honest, and (1-H) denoting the probability that Player 1 cheats. The payoff matrix is now as such:

Now, given that Player 1 is going to steal regardless, Player 2 may have a dominant strategy if (1,H*0.5 + (1-H)*1 +, H*0.5 + (1-H)*-S) is greater than 0. Effectively, Player 2’s decision to split depends on how high he regards his disutility from losing, S, in relation to how much he trusts that Player 1 is honest, represented by H. To analyse this, let’s consider the following:

What we observe in the video is probably the case of Player 2 having a value of H somewhere between 0.5 and 1. We can also assume that the value of S is somewhat high as it is in human nature to be reluctant to be taken advantage of. What we know for sure is that (1,H*0.5 + (1-H)*1 +, H*0.5 + (1-H)*-S) > 0 and Player 2 was convinced that Player 1 was going to steal.Player 1’s decision to split, despite stealing being the dominant strategy for him, was possibly out of altruism or the confidence that his strategy would work and that Player 2 would split.

Player 2 Player 1 Split Steal Split (0.5,0.5) (0,1) Steal (1,0) (0,0)

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