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Political Science 348�Elements of games

The Pearl Harbor Game
Basic questions
Terms

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I. The Pearl Harbor Game

Consider Japan’s decision to attack Pearl Harbor and started a war with the US in 1941
Will illustrate what we need to know in order to write down a game.

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Problem: Japan’s Dilemma

Japan invades China, occupies French Indochina

Current situation is unsustainable: US and British sanction on Oil, Steel, freezing Japanese assets

Possible ways forward?

So imagine it’s 1941, WWII has been going on for two years in Europe. Japan has been fighting a war to conquer China for the last 4 years, the dark orange areas show the territory Japan conquered.

Recently, the western powers, meaning the United States and the United Kingdom has impose a series of sanctions on Japan, stopping the export of oil, and steel to Japan, and freezing Japanese asset in the US and UK. Because Japan , a resource poor country, relies on oil and steel imports from the US, its stock of resource will run out in about 18 months, the sanctions means Japan cannot continue its war in China for much longer. And this is preciously the goal of the United States, by cutting off resource, the US wants to force Japan to abandon its war in China.

This should be a familiar situation today, given this seems to be the strategy that the US and its allies adopt to force Russia to abandon its war in Ukraine by applying economic sanctions.

So how would you get out of the situation if you are leaders of the Japanese Empire in 1941 ? Do we have any WWII historians here?

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A Diplomatic Compromise?

US	Japan
US is negotiating from a position of strength; Japan must give up all its conquest. US is much stronger than Japan, Japan will never dare to attack the US. Sanction exerts increasing pressure on Japan.	Sunk cost: hundreds of thousands have died trying to conquer China, too late to give up. No Incentive to “deviate” from the path of war: Conceding to the demand is as bad as losing a war. Commitment problems: If Japan agree to US demands now, there is no guarantee that US will not demand even more later.

Why couldn’t US and Japan find a diplomatic compromise that both sides can live with?

First, before we talk about war, let’s think about diplomacy. Why don’t the US and Japan just come to some sort of diplomatic compromise?

We need to consider the perspective of the two players, the United States, and the empire of Japan.

From the US perspective, It is negotiating from a position of strength. It’s the US that have the steel and oil, so it has all the leverages. Therefore, there’s no need to compromise. If Japan wants the sanctions lifted, it must give up all its conquest in China and Indochina. The longer sanctions goes on, the weaker Japan will be militarily and economically, so there’s no incentive for the US to cut Japan any slack.

In addition, the US is a much stronger nation than Japan. That means it would be suicidal for Japan to start a war with the US.

Switching to the Japanese perspective. There are also a few reasons, why a compromise with the US or conceding to the US demand is unacceptable.

there’s the issue of sunk cost, after fighting in China for four years. Hundreds of thousands of Japanese had died. They also took a significant amount of territory. To give up now, all the sacrifice in blood and treasure would be for nothing,

If the US demand is a complete withdraw, Some Japanese leader feel that the diplomatic outcome is as bad as losing a war, if diplomatic outcome is no better than war, there’s little incentive for Japan to compromise.

There’s also the commitment problem. That is, even if Japan agree to the US demand now, there’s no guarantee that US will lift the sanction. There’s no guarantee make new demands like Japanese withdrawal from Korea or Taiwan, or the Pacific islands.

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Going North� vs �Going South

Northern Strategy.

Objectives: Attacking the Soviet Union, occupy Mongolia and the Russian Far East

Advantages	Disadvantages
Close to home Enemy (Soviet Union) is distracted, focused on fighting Germany in Europe Neutralize Soviet threat to Japan Help German ally win the world war	Japan has a relatively weak army; the Japanese army has been recently defeated by the Soviets Even Japan can successfully occupy the Russian Far East, these remote region offer little labor or resources

So, we know that diplomatic solution is untenable. There are rough two military alternatives for Japan being discussed in this period, known as the northern strategy and the Southern strategy, describe plans to make new conquest to seize more territories, resource and labor, so that Japan can overcome the economic difficulties of the sanction

The first one is the known as the Northern Strategy, essentially, this strategy means the Japanese army will launch an invasion of the Soviet Union. from occupied territories in Northeastern China,

When it comes to any strategy, we want to think about what are the advantages and disadvantages:

Some of the advantages includes, the battlefield would be close to home. The enemy, Soviet Union is distracted by a war in Europe with Germany. If the invasion is successful, it would neutralize Soviet threat to the Japanese industrial centers in occupied Manchuria. On global level, a Japanese invasion would also help Germany win its war with the Soviets.

But there are also clear disadvantages, for one, the Japan has a relatively weak army compared to the Soviet Union. For example, in 1941, it does not really have any modern tanks at this point and most of its artilleries are old models from WWI era. The weakness of the Japanese army has been exposed in a couple of border wars when Japanese troops in Manchuria was completely defeated by the Soviet Red army. In addition, even if the invasion is successful, the Russian far east is sparsely populated, the resources are not immediately assessable.

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Going North� vs �Going South

Northern Strategy.

Objectives: Attacking the Soviet Union, occupy Mongolia and the Russian Far East

Advantages	Disadvantages
Close to home Enemy (Soviet Union) is distracted, focused on fighting Germany in Europe Neutralize Soviet threat to Japan Help German ally win the world war	Japan has a relatively weak army; the Japanese army has been recently defeated by the Soviets Even Japan can successfully occupy the Russian Far East, these remote region offer little labor or resources

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Objectives

1.Preemptive strike on US Pacific fleet at Pearl Harbor

2. Attack British, Dutch and US colonies in Southeast Asia

Southern Strategy

Advantages	Disadvantages
Enemy (Western powers) are distracted, focused on fighting Germany in Europe Neutralize Western threat to Japan Help German ally win the world war Japan has a very powerful navy undefeated in recent history Some local population might support Japan anti European/American colonialism Resource: Oil and Rubber	Far from home

The second strategy under consideration is the Southern strategy.

This time, instead of invading Russia, Japan would attack the United States, invade Southeast Asia, including the American Philippines, the Dutch East Indians, British Malaya.

So here are some advantages of the southern strategy:

The enemy, in this case, Britain,the Netherlands are also distracted by the War in Europe and middle east. Most of these colonies are either undefended or poorly defended. For example, almosy the entire Australian army was sent to help the British in North Africa, with noon left to defend Australia or its colonies.

Successful invasion, would neutralize the threat of the Western powers to Japan by pushing them far from the Japanese home isles and Asian mainland.

Like the northern strategy it could help German win the world war.

Crucially, Japan has two unique advantages when it comes to the southern strategy

Japan has a very strong navy, it not only has a fleet of battleships but also has a cutting-edge aircraft carrier fleet.
there’s a lot of resentment against European and American colonial rules in Southeast Asia, when Japan invades these colonies, they can count on some level of local support or collaboration.
And most crucially perhaps, Japan can capture oil fields in Brunei and Malaya, which provides direct remedy for the economic sanctions’

The obvious disadvantage is that southern strategy requires logistic support for troops in far-flung region, a lot of maritime transportation and amphibious operations that are difficult to do.

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Objectives

1.Preemptive strike on US Pacific fleet at Pearl Harbor

2. Attack British, Dutch and US colonies in Southeast Asia

Southern Strategy

Advantages	Disadvantages
Enemy (Western powers) are distracted, focused on fighting Germany in Europe Neutralize Western threat to Japan Help German ally win the world war Japan has a very powerful navy undefeated in recent history Some local population might support Japan anti European/American colonialism Resource: Oil and Rubber	Far from home

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South
Advantages	Disadvantages
Enemy (Western powers) are distracted, focused on fighting Germany in Europe Neutralize Western threat to Japan Help German ally win the world war Japan has a very powerful navy undefeated in recent history Some local population might support Japan anti European/American colonialism Occupation of Southeast Asia can provide a large amount of oil, rubber, and labor to support Japan’s war effort. Resource: Oil and Rubber	Far from home

North
Advantages	Disadvantages
Close to home Enemy (Soviet Union) is distracted, focused on fighting Germany in Europe Neutralize Soviet threat to Japan Help German ally win the world war	Japan has a relatively weak army; the Japanese army has been recently defeated by the Soviets Even Japan can successfully occupy the Russian Far East, these remote region offer little labor or resources

Comparison of alternatives along these dimensions

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South
Advantages	Disadvantages
Japan has a very powerful navy undefeated in recent history Some local population might support Japan anti European/American colonialism Occupation of Southeast Asia can provide a large amount of oil, rubber, and labor to support Japan’s war effort. Resource: Oil and Rubber	Far from home

North
Advantages	Disadvantages
Close to home	Japan has a relatively weak army; the Japanese army has been recently defeated by the Soviets Even Japan can successfully occupy the Russian Far East, these remote region offer little labor or resources

Comparison of alternatives along these dimensions

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Why did Japan adopt the Southern Strategy?

Agreed that chance of success was low

Lack of alternative

Northern strategy is high risk, low reward,
Diplomacy fails

Limited success of Southern strategy provide economic benefit even if war cannot be won outright.

Strategy is often about choices between bad and worse.

So, why did Japan adopt the Southern Strategy?

Are they so overconfident and naïve that they think they can easily defeat the US? Not really.

1940, Japanese planners had calculated that the industrial capacity of the United States was 74 times greater, and that it had 500 times more oil. So if there’s a long war, Japan is very unlikely to win. And Japanese leader understand that if they pursue the southern strategy, the chance of success is low.

But, they choose the southern strategy because the alternatives are even worse. The north strategy is high risk and low reward. Diplomatic compromise with the US is impossible, conceding to US demand is unacceptable.

In addition, even if the South Strategy is not completely successful in rapidly defeating the US, as long as Japan can achieve limited success in occupying the resource producing areas of SEA could provide more resources, and labor for Japan.

Japan’s dilemma in 1941, also shows that strategy is often about choose the lesser evil.

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Factors that go into making this kind of decision

Comparison of alternatives along these dimensions

1. Probability of success or failure

1.1. The Pearl Attack: secrecy, untested tactic (carrier warfare)
1.2. War with the US: resources, labor, industrial capacity

2. Expected benefits of success (e.g. resource, labor)

3. Expected costs of different policies

Include direct cost
opportunity costs (the advantage of forgone alternative)

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Strategic Games

Games, or strategic games, occur when it is necessary to take into account the responses of others.
Everyone is aware of that others are taking their responses into account.
These are called strategic decisions

game theory is the principal tool for studying them.

Now let’s take a step back from the example and look at what makes the US-Japan interaction a strategy game.

The key characteristics is that the strategies of the two nations are interdependent. No one is making decisions in isolation. US has to decide how much it would demand in exchange for dropping sanction. Based on what the US demand is, Japan has to decide whether to go to war, going north or south. Each plater’s decision takes into account the response of others.

The first question in the problem set is going ask you what’s the difference between decision and strategic game, decision independently, and strategic game interdependent. For example, if you are considering buy the new iPhone, based on your budget and preference, that’s an independent decision. But if you are considering buy the new iPhone to flex on your friends in some sort of conspicuous consumption competition that would be strategic game.

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II. Basic questions

Begin to formalize this story by identifying the elements of the problem.

Conflict of interest
Simultaneous or sequential moves?
Can players change the rules of the game?
Information
Repetition
Enforceability*

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1. Conflict of interest

Players’ interests may be in total conflict: zero-sum or constant-sum game.

Some quantity needs to be divided up: a gain for one is a loss for another.
A purely distributional problem. (e.g. Fight over territory)

Usually in economics and politics, deals are possible that make all players better off

positive-sum. (e.g. Trade Agreement)

Games that combine conflict of interest and benefits from cooperation are called mixed-motive.

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2. Timing of moves

A move is the action that a player can take at some point in the game.
Moves can be sequential: one player goes first, the other responds (Japan decide whether to go to war after seeing the diplomatic result).
Sometimes moves are essentially simultaneous.
Also characterize moves as simultaneous if the second player doesn’t know what the first has done.

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2. Timing of moves: Simultaneous

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2. Timing of moves: Sequential

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3. Can actors change the rules of the game?

We will typically assume that the rules of the game are fixed
However, in politics, it is often the case that certain actors can change the rules of the game
Examples:

Agenda-setting (e.g. UNSC Draft Resolutions)
Creating institutions

If the rules can be changed, this involves specifying a pregame that happens before the game itself

E.g., creating the rules of an institution, such as the WTO’s dispute-resolution mechanism.

The third question we need to answer is whether players can change rules of the game.

In real world, players sometimes have the opportunity to change rule of the game. One example is the United Nations Security Council, Whenever there’s a crisis, members of the security council can propose draft resolution on what to do about it. The draft solutions never contains all possible strategies, member only propose the policy they prefer, and everyone can only vote yes or no. In the Korean War for example, the UN resolution 84 calls for the establishment of a unified UN military to fight the North Koreans. Members either support or oppose it. Other possible options like economic sanctions, mediations, are not being considered. Permanent member of the UNSC can also eliminate options they dislike using their veto power.

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4. Information

Do both players have full information about the probabilities and payoffs in the game?

If so, this is called a full or complete information game.
If not, this is a game of incomplete information.

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Incomplete Information

If information is incomplete, do both players share the same information?

If yes, this is a game of symmetric information.

e.g. is it going to rain before the Battle of Agincourt (1415)?

If no, this is a game of asymmetric or private information.

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Asymmetric Information

In asymmetric information games: I know my own payoffs, but you don’t.
Bluffing, signaling, and screening become central.

Asymmetric information is when some players know more than other players. Let’s look at this game of red wedding. Suppose we have a wedding banquet in the medieval period, there’s two players, the host of the banquet and the guest. The guest really wanted to attend the wedding, because it cement the alliance between the two houses. But there’s a chance that the host might try to murder the guest. The host make up their mind first, deciding whether to murder or not. If there’s prefect information, the choice of the guest is very straightforward, if there’s going to be murder, guest wouldn’t attend, no murder, the guest would attend.

The problem is, the guest don’t really know whether they are on the left side of the tree where the host is honest and wont murder them, or the right side of tree where they will be murdered.

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Solutions to Imperfect Information

Signaling occurs when a better-informed player takes steps to reveal information.

Screening is used by the less-informed player.

So how do we overcome with the asymmetric information problem? Essential both players, the more informed and the less informed, can take action to reveal more information.

For example, an honest host could signal their honesty by opening their castle and allow an army of their guest to enter. This put themselves in a vulnerable position to show the guest they have no intention to do harm. You are going to hear a lot about this type of behavior called costly signal.

The flip side of signally is screening. This time, it’s the less informed player who takes the initiative. Suppose, the guest is worrying about being poisoned by the host at the banquet, a screening mechanism they can adopt is to ask the host to drink their own beverage. The idea is that if the host knows the drinks are poisoned, they are definitely not going to drink it. So by observing host behavior, the guest can differentiate the honest and dishonest host.

In fact, it was said that originally toasting was a supposed to be screening mechanism against poisoning.

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5. Repetition

Some games are one-shot

played only once.

Some games played repetitively.

Most international interactions are repetitive.

Games played over time create new dynamics:

reputation
trading off short-term benefits and long-term costs.

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6. Enforceability*

Sometimes external (third-party) enforcement is available

E.g. courts to enforce contracts.

This can increase the range of mutually-beneficial deals that can be reached

the “right to be sued.”

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Enforceability*

In IR, unusual to have 3d-party (neutral) enforcement available.
So, any enforcement has to be done by the players themselves

agreements must be self-enforcing.

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III. Terminology

Strategy
Payoffs
Common knowledge
Equilibrium

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Strategy

A strategy is a complete plan for playing the game.

If game is one-shot with just two possible actions, the description of the strategy is simple.
If repetition or multiple actions, complex because you have to specify how to act in every conceivable contingency.
Rule of thumb: you have appropriately described a strategy if you could write it down for someone else, and they would play exactly the same way as you.

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Payoffs

Example: Lunch Game

A payoff is how much each player value each outcome

Payoffs tell us whether the game is coordination, zero-sum, or mixed-motive.
Sometimes, adequate just to rank outcomes (1, 2, 3 …).
At other times, need more precision and so have to attach a numerical scale to outcomes (like dollars).
Payoff can be material or nonmaterial

Payoff is probably the most important aspect that defines a game. Payoff describes how much player value outcome.

Consider the situation that you are your friends are going to grab lunch after class. We are chosen between three restraint options, pineapple pizza, burrito, or pasta.

Alternatively, we could have a coordination game, everyone do not care what they eat, they just want to have lunch with their friends, so all that matter is everyone picking the same restaurant.

The payoff will tell us whether game is zero-sum. For example, if you decides to have pizza, and everyone is sharing a single pizza, then one person consume more mean other players must consume less.

A game can be mixed motive, where players care about coordinating with their friends, but they also hope they everyone pick their favorite type of food.

Sometimes we cannot quantify payoff exactly, Payoff can be a rank preference of outcome. You can tell , you prefer pasta to burrito to pizza for example, by assigning value 3, 2, 1 to each the three types of food respectively.

And lastly, payoff is subject, one person may love pineapple pizza, and others rather die before eating it.

Other times, we can actually quantify payoff preciously, suppose you are paying for everyone’s lunch, and you want to spend less little as possible. You can just use the price of food to specify your payoff.

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Payoffs and Risk

Payoffs captures everything associated with an outcome that an actor cares about.
In assigning payoffs, sometimes have to think about players’ attitudes toward risk.

Are they risk-averse or risk-neutral?
Would they prefer to take a risk rather than choosing a safe but possibly second-rate outcome?

Would you take $1000 right now or enter a lottery with 0.00001 chance of winning $200 million?

Two additional notes on payoff.

One common critique of game theory in recent years is that it’s incorrect to assume everyone as maximizer of self-interest.

So increasingly, we want to model the psychological, irrational factors. For example, an altruistic player caring about how the outcome affects others, a revengeful player may just want others to suffer, this has to be reflected in their payoffs.

Another issue is risk attitude., we assigning the payoff, we need to consider how much risks the players are willing to take.

For example: consider choice between getting 50 dollars for sure and a 50/50 chance of getting $100 or nothing, would you prefer one or the other. Expected value is identical; a risk-neutral player would be indifferent. But a risk-averse actor would prefer the sure thing. This would have to be reflected in the payoffs for the game.

Players could also theoretically be risk-acceptant. For risk-accepting the riskier an outcome is, the amore attractive it is. For example, they would prefer a 10 percent chance of getting 1000 dollar to getting 100 dollars for sure.

At a glance, risk-accepting may seem irrational, but if you think about it, there are entire business models, like gambling and loot box in games that are built on risk-acceptance. So it’s actually a common human tendency.

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Common knowledge of rules

Players must all share a common understanding of the rules of the game, even if there is incomplete information in the sense discussed earlier.

Definition (more formally): Any information that all players know, that all players know that all players know, and so on, is common knowledge.

Need to agree on:

what moves available
order of moves
who is playing
that all players are rational
Also, know that others share all these beliefs, and they know that you do, etc.

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Equilibrium

The point of game theory is to identify equilibria.

Definition: each player is using the strategy that is a best response to the strategy being used by the other player.
Given the strategy of each, neither has an incentive to unilaterally change their strategy (deviation).

Equilibrium is the outcomes of the game, when all players do what’s best for themselves.

More formally, each player is using the strategy that is a best response to the strategy being used by the other player.

It’s worth noting that equilibrium is not always the ideal/good endings, Usually some of the most interesting games in international politics have tragic equilibrium outcomes. That is, we have outcome that would make everyone better off, but that good ending cannot be achieved. For example, the one-shot Prisoner dilemma is tragic in the sense that we can make both player better off if they cooperate, but cooperative outcome is not an equilibrium outcome.

That concludes the lecture today. Just a remember that the first problem set is due next Thursday Sep 22, the first problem set is short and essay should take you 15-20 minutes, and you should be able to get started. If there’s no question, I’ll see you next week.