Although often intertwined with oligopolies, the subject of game theory deserves independent recognition given its application to a variety of other areas apart from economics such as behavioral biology and sociology. Game theory is, in its broadest sense, studying decision making, with the goal being to model competing players and figure out the mathematically optimal decisions.
The Prisoner’s Dilemma
You (A) and your fellow accomplice (B) are both arrested and held in separate interrogation rooms. While the prosecutors do not have sufficient evidence showing that you robbed the house, they have security camera footage showing that you trespassed on private property. The police aren’t satisfied with that, and so they offer each a bargain: tell the police that the other committed the crime, hence betraying your robber-mate, or exercise your right to remain silent. With this, there are 4 possible outcomes:
A and B betray each other, and so they're prosecuted for breaking and entering but, since they both confessed, are sentenced to 5 years in jail
A betrays B but B remains silent, and so B is prosecuted for breaking and entering - 10 years in jail - while A is set free
A remains silent but B betrays A, and so A is prosecuted for breaking and entering - 10 years in jail - while B is set free
A and B both remain silent, and so both get away with just the trespassing offence, meaning 2 years in jail for each of them
What should be done? If we look at it from the perspective of either of the robbers, scenario (1) seems the most likely - betraying the other yields the greatest reward, no matter what the case. If we observe the alternative cases:
A betrays B, B remains silent, and so A is set free while B gets 10 years in jail (bad from B’s perspective)
B betrays A, A remains silent, and so B is set free while A gets 10 years in jail (bad from A’s perspective)
A and B remain silent. They still each get 2 years in jail while either one of them could’ve been set free - a huge chance blown
Even if A and B betray each other, that’s still preferable than either one of them getting 10 years and the other being set free. If one of them is going down, it’s better to take the other down with them. But what’s interesting about the prisoner’s dilemma are the conflicting incentives at play. Both robbers can minimize jail time by keeping their mouths shut (only 2 years for each of them), but each of the individual robbers can walk free if they betray the other.
The “solution” to this (assuming we’re still A) is to betray - no matter what B does, we’ll likely be in a better position than if we stayed silent. But this version of the prisoner’s dilemma assumes only one move to make, that is, you either betray or stay silent and that’s the end of it. What if we could play the prisoner’s dilemma multiple times? How might that affect the strategy?
Iterated Prisoner’s Dilemma
Instead of just one move, the iterated prisoner’s dilemma allows players to choose either betray or stay silent again and again. A small extension, but one that significantly changes (wrong adjective?) how one ought to approach the game. Now that each player is repeatedly faced with betrayal or staying silent, this presents the opportunity to read your counterparty and understand their behaviour.
Unlike the original prisoner’s dilemma, the best strategy is to actually start out cooperative, meaning you stay silent. Assuming your counterparty does the same, this means you both land 2 years in jail. From here the strategy addresses what you should do if met with either of the 2 possible scenarios: if the opponent betrays in one round, you betray in the next. But if the opponent cooperates in one round, you do so in the next.
Let’s start at the beginning, with you being A and your counterparty being B.
Round 1: A cooperates, B betrays. A gets 10 years in jail, B is set free
Remember the strategy: if your opponent betrays you in one round, you betray in the next:
Round 2: A betrays, B betrays. Both get 5 years jail time
A and B, seeing as the other has attacked them, are now going to again retaliate:
Round 3: A betrays, B betrays. Both get 5 years jail time
Doesn’t seem fun, does it? Assuming both players continue to follow the retaliation rule, it’s just going to be them both getting 5 years jail time from here on in. Now they can change the strategy to something more complex (which we will touch upon) or they could just cooperate in the first round:
Round 1: A cooperates, B cooperates. Both get 2 years jail time
Remember the strategy: if your opponent cooperates in one round, you do so in the next
Round 2: A cooperates, B cooperates. Both get 2 years jail time
Round 3: A cooperates, B cooperates. Both get 2 years jail time
Even from B’s perspective, who initially betrayed A and was set free in Round 1 of our first example, cooperating means less jail time in the long run. This remarkably simple technique is what’s called “Tit for Tat” and it’s a common game plan for the iterated prisoner’s dilemma. But why is it so effective? There are actually a few reasons. Firstly, you start off nice, hence paving the way for a cooperative relationship between you and your opponent. Secondly, it lets the other player know that they can’t just push you around. If they stab you in the back, you do the same in the next round. Thirdly, it’s forgiving - if your opponent goes back to cooperating, so do you.
Granted, tit for tat is the superior approach only under the iterated prisoner’s dilemma we’ve given here. What if we have only 3 rounds to work with - we cooperate on the first 2, but then our opponent betrays us on the third one and we can’t get him back. Those scenarios, however, (and many others) are for another time. We’ll look at more complex situations in the future.
Econ IRL:
This week’s paper, published this very month in fact, explores the idea of firms entering a market early in order to prevent future entry and limit competition. The researchers look at the US drive-in theatre market in the mid 20th century to observe the effects of strategic motives of the industry structure of new technologies, with this case being drive-in theatres.
They find that firms entering early into a market to prevent future competition actually increased the number of entrants by as much as 50% (at least in mid-sized markets), but this didn’t affect the number of firms in said markets in the long-run. Additionally, entry costs were increased by 5% and the firms’ expected value decreased by 1%.
These results highlight an interesting predicament when examining market structure and what that means for consumers. On one hand, firms entering early may benefit consumers due to lower prices and more rapid innovation. But on the other hand, if this early entry is simply firms trying to deter future competitors, then it may lead to a more monopolistic market.
‘Till next time,
SoBasically