Nash Bargaining Game

• Inventor of Game: John Forbes Nash

You’ve likely seen a lot of the “Nash equilibrium” stuff within many game theories or in other economics content. That comes from John Forbes Nash, who also invented the Nash Bargaining Game. You might know it best today as “cooperative bargaining.” Today, Nash’s bargaining solution has become one of the more infamous game theories economists and even social scientists discuss. This is a situation where you see a two-person bargaining problem that satisfies the accepted terms of scale invariance, symmetry, efficiency, and independence of irrelevant alternatives. Within the game, two players will play to model bargaining interactions.

Of course, both players will demand a portion of something. This is usually going to be money, but the goods used can differ. If the total amount requested by the players is less than what is available, both players will get what they want. If the total amount is greater than what is available, neither player gets what they want. You are presented with a non-cooperative demand game with two players that are uncertain about the best possible payoff. You simply do not know what the other player can offer and they do not know what you can provide, so many believe it is best to ask for less to guarantee you get something.

Peace-War Game

• Inventor of Game: Unknown

The Peace-War Game was usually played by academics via computer simulation to study cooperation and aggression strategies. Due to the peacemakers becoming richer over time, it was clear that making war had greater costs than some assumed. Many game theories can open our eyes to things that surprise us like this. The only strategy that acquired wealth rapidly was “Genghis Khan,” who was historically a constant aggressor that made war constantly to gain resources. Using this strategy could benefit players in simulation. However, it was simply not feasible to do this as you risk a lot more than you gain unless you can guarantee victory.

That led to the “provokable nice guy” strategy, which is a peacemaker until they are attacked. Players will continue to gain wealth doing this by cooperating with each other, which then eats away at the potential profits of constant aggressors. The best deterministic strategies were usually reciprocal altruism, tit for tat, and the provokable nice guy. Therefore, the best strategy to take, at least initially, is to make peace. After this, you can switch it up, where you might do “tit for tat with forgiveness.” As in, you make war then on the next move make peace anyway. That allows players to escape from wasting resources on retribution cycles.

Traveler’s Dilemma

• Inventor of Game: Kaushik Basu

In the Traveler’s Dilemma, an airline loses two suitcases that belong to two different travelers. Both are identical suitcases and contain identical antiques. The airline manager is now tasked with settling the claims of both travelers. He must tell them that the airline is only liable for a maximum amount of $100 per suitcase. However, he’s unable to find the exact price of these antiques. Therefore, to determine a proper appraised value of the antiques, the manager decides to separate each traveler to speak with them alone. He asks them to write down the amount of the antique value. He also gives a rule that it must not be less than $2 and no larger than $100.

The manager claims if each traveler writes down the same number, then he will see this as the “true” value of the antiques and reimburse both travelers with that exact amount. Yet if either writes down a smaller number than the other, the smaller number will be seen as the true value. Both will be given that number along with $2 extra being paid to the one who wrote the lower value while $2 would be deducted from the person who wrote down the higher amount. The question is: what strategy should the travelers employ? Most would say to write down the maximum amount, as this would generate the highest profit for both and they’ll be given the same number without either seeing a deduction.

Keynesian Beauty Contest

• Inventor of Game: John Maynard Keynes

The Keynesian Beauty Contest is one of the most well-liked game theories around. Invented by John Maynard Keynes, he decided to come up with a game theory that could properly explain price fluctuation in equity markets. In his 1936 book, The General Theory of Employment, Interest, and Money he describes a simple beauty contest. In this contest, people are rewarded for selecting the most popular faces among all players. This is being done over the more common concept of which they might personally believe to be the most attractive. Essentially, they are picking the person they feel the others will pick.

These rational agents (the people) are given 100 photographs and are tasked with picking the six most attractive faces. Those who pick the most popular faces get a reward. The more common choice would be to pick the people that are attractive to them, but a sophisticated contestant might wish to maximize their chances of winning. Therefore, they would need to know what the majority perception of attractiveness is, then make their selection based on that. The hiccup in this is that one must consider the differences in attractiveness we all have that differ from the norm. This game theory has been utilized in many forms, especially in the stock market.

The Kobayashi Maru

• Inventor of Game: Spock (Gene Roddenberry)

This is Science Sensei, if you thought we were going to avoid using the Kobayashi Maru from Star Trek, you were sadly mistaken. This game was utilized in the Starfleet Academy, introduced by Spock. Of course, Spock comes from the Vulcan race of people who use logic to determine their actions across all aspects of decision-making on their planet. In this game, your character is being tested the entire time. The actual game will always result in a no-win scenario, but the players or cadets are unaware of this going into the simulation. The goal of the exercise is claimed to be to rescue the civilian ship known as the Kobayashi Maru.

It is damaged and stranded in dangerous territory. The cadet being evaluated, usually the Captain in the simulation, must decide whether to attempt to rescue the ship or not. They could do so, endangering their own ship and crew, or leave it behind to see certain destruction. Those attempting to rescue the ship will be hit by an enemy force that will end them. There is no way to win unless you do as James T. Kirk did. He was the only cadet to defeat the test…because he cheated. Kirk knew he could not win, so to avoid certain demise, he changed the conditions of the test itself.

Volunteer’s Dilemma

• Inventor of Game: John Forbes Nash

The Volunteer’s Dilemma is one we’ve likely all been faced with, even if we do not realize it. Thus, it is one of the most relatable and timeless game theories. This game gives you a situation where each player can make a small sacrifice that benefits everyone or wait in the hopes of benefitting from someone else’s sacrifice. Yet “sacrifice” should not be seen as one choosing to end their life each time. It might just be an inconvenience issue for them. One example of this might be that the power goes out for an entire block. Surely, there must be a problem for everyone considering it is not just YOUR power that is off.

Therefore, one person can call the electric company so they will come by and fix the issue for everyone. However, there was still a cost one has to give up when they call. It might only be their time, some sort of effort, etc. Yet there is still something given up that others did not have to sacrifice. Thus, if one person volunteers then everyone else benefits. This has often been cited as an issue for the public good. Unless the volunteer is guaranteed some benefit, they might feel they will benefit most by free-riding. There is also an issue of the bystander effect, where people see but do not report an incident because it doesn’t benefit them.

Prisoner’s Dilemma

• Inventors of Game: Merill Flood, Melvin Dresher, & Albert W. Tucker

A lot of the game theories we referenced previously often act against or differently from the Prisoner’s Dilemma. While the game theory has been heavily expanded upon over the years, the initial game follows two completely rational individuals that may or may not cooperate with each other. Even if it is in their best interest, they might still be at odds. Within this dilemma, two members of a criminal enterprise are arrested and put in prison. Each prisoner is somehow in solitary confinement, which would prevent them from talking to one another. The prosecutors of this case lack enough evidence to convict both on a principle charge. However, they have more than enough to convict both on a lesser charge. To hopefully get more out of this, the prosecutors offer both prisoners a bargain.

Each prisoner could betray the other by testifying that the other prisoner committed the crime. Yet they could also decide against this by remaining silent. If both betray the other, each serves a two-year sentence. If one betrays the other, the betrayer will be set free while the betrayed gets a three-year sentence. Meanwhile, if both remain silent then they will each only serve one year on the lesser charge. Which decision is best? Many believe remaining silent works best because both of you lose if both of you talk. You cannot know what the other will do, so it seems like talking makes the most sense. However, remaining silent offers a better outcome, as you could not know what the other will do. If you both talk, you get a larger sentence than if you both remain silent.

Sources:

Stanford University

University of Wisconsin-Madison

Massachusetts Institute of Technology

University of California – Irvine

Columbia University

Cornell University

University of Virginia

University of Michigan

Barcelona School of Economics

Journal of Interdisciplinary Economics

National Library of Medicine

Star Trek

World Rock Paper Scissors Association