Evolutionary Game Theory

• Inventors of Game: John Maynard Smith & George R. Price

Some game theories are mostly about mathematics, whereas the Evolutionary Game Theory gives us a biological connection to go with that. In fact, this specific game theory has a lot of importance in the world of biology. As it helps to define contests, strategies, and analytics that model Darwinian competition. In most game theories, you’re usually focusing more on the classical model that only deals with the strategic payoffs of something. But this game has to focus mostly on the dynamics of strategy change overall. This is key to remember, as this means strategies used in one period might not be applicable in the second period.

This game has been critical in explaining the basis of altruistic behavior, such as how the male interacts with the female. Whether or not the female is larger or smaller could play a factor in this among many other things. Due to the MANY versions of evolutionary game theory, it would be tough to go over all of them. Rather, we’ll give you the basics of each. It always starts with a competitive situation that is only resolved when a change occurs. That might mean one must alter their strategy or risk potentially both or all players meeting their early demise. That is evolutionary because if something did not change or adapt, life could not continue to exist.

Dollar Auction

• Inventor of Game: Martin Shubik

The Dollar Auction is one of the most well-known game theories. To play, there must be one auctioneer who chooses to auction off one single dollar bill. It will always be a one-dollar bill too. The winner will get this bill. Yet the second-highest bidder will lose the amount they bid. In turn, this makes that person the biggest loser in the auction itself. Naturally, the bill could go for any amount. To get some money out of this for the auctioneer, 5 cents is the lowest that can be bid. It is therefore smart to bid this small sum to make a 95-cent profit. Yet others could bid higher at 10 to even 50 cents. One would not want to lose money, but you might want to.

The real goal is to not only win the bid but cause the second-highest bidder to lose everything. For example, if the highest bidder goes to $1.10 for their bid, they did lose 10 cents on this. If the second-highest bidder bid 90 cents, they have now lost the full 90 cents while the winner only lost 10 cents. Therefore, the true game here is not just to win but to screw over the second-highest bidder. Considering you’re pushing them to keep up with you. The auctioneer usually profits in the end, as they get BOTH the winner and second bidder’s money. That could add up to be more than the dollar amount.

Cournot Competition

• Inventor of Game: Antoine Augustin Cournot

This game revolves around the industry structure where companies compete on the amount of output they’ll produce. Just like with other game theories like it, companies must decide on what they do independently and at the same time. For this to work, more than one form of all firms involved must produce a product, without differentiation. None of the companies can cooperate or collude. Each must have market power, so the firm’s output affects the price of the goods. The number of firms must be fixed. Firms will compete in quantities rather than prices, acting strategically as they seek to maximize profits.

However, each of the competitor’s decisions will affect everyone else in some way. Each firm will want to maximize profits in spite of not knowing what decisions will be made by others. Each firm’s output decisions will not have an effect on the decision of its rivals, as they’ll find out afterward. All firms will know the total number of firms in the market and will take the output of others as given. In this game, demand equals the total quantity produced by all firms. Each must then take the quantity set by its competitors, evaluate the residual demand, and then react as if they are part of a monopoly.

Poker

• Inventor of Game: 1800s French Settlers

You might wonder how the game of poker could somehow be one of the most notable game theories. You likely also want to know how this could be one of the most mind-boggling game theories on top of that. However, for those that know the game of Poker, you’re well aware of the strategy one must consider. Poker is not just a fun game to play with the boys. It’s also a game where you must consider several different issues and base your decisions on them. Things to consider will, of course, be things like the hand that you have, the chips you possess, what your opponent(s) have to play, and much more.

David Sklansky famously introduced a fundamental theorem of poker. Where he referenced how poker is a game of decision-making directly in the face of incomplete information. This is why it is a game of risk for those that play. Every time you played your hand the way you would if you could see your opponent’s cards, you gain. Every time your opponents play their cards from the way they would play them if they could see your cards, you gain. However, on top of all of this might be the strategy of bluffing or slow-play, which adds in the element of deception that alters how your opponent(s) play. Beyond this, Poker also might include things like pot odds among many other potential issues a player must face.

Deadlock

• Inventor of Game: William Poundstone

It is likely that if you’re reading this, you know what the term “deadlock” means. However, if you’re unaware of the term, it means that there is a state of inaction or neutralization. That neutral position could be due to several different factors, but almost always has to do with some form of equal power or uncompromising person/faction. Thus, nothing can move beyond a mere standstill. You might know this best from sports when a game ends in a tie. In the world of game theories, the Deadlock game involves an action that is mutually the most beneficial to all players, and must also be dominant.

Due to the fact that all players would win as long as the actions benefit everyone mutually, there is less interest. People want to see some form of conflict between self-interest and mutual benefit. However, what is lost in all of this is that a deadlock game can also heavily impact economic behavior. It can even induce or formulate changes to the equilibrium outcome within a society. The real loss economically here is that a deadlock can reduce potential bargaining power. To break from it, one can use their business power to put a price on the status quo, introduce a process move, and/or add appreciative moves. The latter of which is beloved by buyers.

War of Attrition

• Inventor of Game: John Maynard Smith

War of Attrition in the world of game theories can be somewhat connected to the regular term. In this game, you’ll be given dynamic timing where the players will choose a time to stop and then trade around the strategic gains from outlasting the other players. This will involve the real costs expended with the passage of time overall. This is a lot like the evolutionary game theory but is strategically comparable to the mixed evolutionarily stable strategy. In this game, players can bid any number they’d like in this all-pay, sealed-bid, second-price auction. One’s bid is even permitted to exceed the value of what you’re bidding for.

It might seem crazy to bid over the item’s value, as one would usually not want to exceed the assumed value of any item. That’s just wasting money. Yet you should keep in mind that each player only pays a “low” bid. This is why it would likely be best to bid the maximum possible amount rather than one equal to or less than the value. However, if both players involved bid above the value, then the highest bidder does not win as much as they just “lose less.” Whereas those who bid less than the value will still lose, but they’d lose less than those who might have bid higher than the value who also lost. In the end, there is no beneficial bid in all cases, making this game very difficult as there is literally no dominant strategy to employ.

The Free Rider Problem

• Inventor of Game: Heinz Kohler (originated term)

The term “free rider” is likely one you heard in history class a few times. This game was essentially formulated to find the best strategy to deal with the free-rider problem. Data proves to us that in many situations, all individual members of a group can benefit from the efforts of each member. All can then benefit from collective action. As an example, if everyone pollutes less by driving our cars less, then we ALL benefit from the reduction of harmful gases reducing in the air we breathe. We might even pay for this over other things, and as long as it works out, we’re good. But if something costs more than it is worth, it is no longer a collective good.

For example, you might pollute less but that does not matter enough for anyone, especially you, to notice. Thus, you might not contribute your fair share toward not polluting the atmosphere. However, if it improves in spite of your contribution, YOU are a free-rider here. You’ve seen benefits without putting your fair share or anything into this. Within the world of game theories, the free-rider problem will usually always result in a negative issue where some benefit by doing nothing while others lose in the hope of some benefit. It might seem dumb to pay money out of our pocket while others who put in $0.00 then benefit from it. However, if this is something like a road for example, then everyone needed to have this. Therefore, the benefit is so great that it exceeds the potential loss within the free-rider issue.

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