This is the first article of a series called “Economics is Everywhere” in which I explain how we can apply and use economics theoretical concepts in our day-to-day life. In this first article, I will explain how game theory can help us determine the most rational strategic decision in a Sidemen video – a video from a group of English youtubers with 13 million subscribers.
(The relevant extract start at 43 minutes)
In the video: $100,000 Split or Steal (extract above), each of the two remaining players face a decision on which depend the repartition of the $93,000 between each of them:
- Each of them can either chose to “split” or “steal”
- If both players chose to “split”, the $93,000 will be equally split between them
- If both chose to “steal”, each of them will get $0
- If one player decides to “steal” while the other decides to “split”, the “stealing” player will get all the $93,000 while the “splitting” player will get nothing
It might seem impossible to predict what players will be doing in this situation, but game theory, which is the study through mathematical models of strategic interactions among rational decision-makers, can help us determine what rationale players would choose between “split” and “steal” in this situation.
First, we must make sure that we are studying a game in which game theory applies. In game theory we need:
- The players of the game: KSI and Vikstar, the two youtubers in the video
- The information and actions available to each player at each decision point: there is only one decision point in this game and both players do not have any information about the other player choice, execept that both players have the same payoffs and decisions.
- The payoffs for each outcome: each payoff is well defined (as summarised in the table below)
Now that we know that we can use game theory to solve this game let’s use a table to do so.
When solving this game we will assume both players are rationale.
From this table:
- If player 1 plays “split”, player 2 will play “steal” as his payoff is higher ($93,000 compared to $46,000)
- If player 1 plays “steal”, player 2 is indifferent between playing “split” and “steal” as his payoff will be $0 in both cases
As this game is symmetrical, we can deduce exactly the same thing for player 1.
In game theory, “split” is a weakly dominated strategy that is a strategy that will never yield the highest payoff whatever the other player plays. In this case, a rationale player should never play a weakly dominated strategy. Therefore, neither KSI nor Vikstar (the two youtubers) should play “split” and the game should end with both player playing “steal” – KSI made, therefore, the best decision.
The outcome (steal, steal) is the rationale outcome and this outcome yields a payoff ($0,$0), which is the lowest combination of payoff in the table. Both players will be better off if they collude to both play “split”, resulting in a payoff of ($46,500, $46,500). Player can only collude when the game repeats itself. For the collusion to work, the cost of deviating once (playing “steal” while the other player plays “split” as agreed) should be higher than the payoff of this play (+$46,500).