The coronavirus caught us off guard. Republicans blame China. Democrats blame Trump. President Trump blames Governor Cuomo and he slams Trump in return. Fox News defends the president’s actions, while CNN attacks his administration. Some people think economic activities must resume; others believe reopening states is akin to murder. All this may seem completely irrational. But every player is acting rationally. Game theory can show us why.
The Rationality Within the Irrationality
In 1944, John von Neumann and Oskar Morgenstern came up with an innovative approach to economics: game theory, the study of the ways in which the interacting choices of agents produce outcomes that reflect their preferences (or utilities).
Game theory is now applied to everything from economic and social policymaking to politics and war. By modeling situations as games, theorists can show that the choices made by agents (players) are often rational and the outcomes predictable.
In economics, a game is a situation in which the outcome for all agents depends on the choices of each agent. But no single player can choose an outcome: players can only choose their own strategies and try to guess what others will do. The final outcome might not have been intended by any single agent.
Game theory assumes that individuals are rational and that, prior to action, players conduct a decision-making process, in which they rank their preferences from best to worst and then act in the way they believe will bring about the greatest utility (positive impact), regardless of whether those actions are correct by some objective standard.
To understand these choices, game theorists draw a payoff matrix, which lists the possible outcomes arising from the different actions the players might take.
These games are useful in the real world, to model real politics.
Game 1: Warfare Dilemma (Republicans vs. Democrats)
In early April, Republicans attempted to pass a small business Coronavirus relief package in the US Senate. However, Democrats blocked the bill in order to introduce their own measures. This took a week. Republicans criticized them for playing politics and holding up the bill—many small businesses went bankrupt before the law was signed. Wouldn’t it have been better for everyone if the two parties had cooperated and rapidly passed a bipartisan bill? Probably. So why didn’t they?
If Democrats and Republicans collaborate, they both benefit: a bill with common terms is approved in a timely fashion and the small businesses get the help they desperately need. Let’s assign 7 points to each party for that. But if Republicans manage to pass a narrower law more quickly, they can say that they helped small businesses, without abandoning their customary budget restrictions; and, if Democrats successfully introduce everything they want in the bill, they can put forward their agenda of public spending. In these situations, let’s say the winner gets 10 points and the loser receives -3 points. If neither party is able to get everything it wants, we have a tie. For instance, both waste time coming to an agreement on some measures (not all), increasing the cost and moderately expanding funding coverage. Let’s assign zero points to this case—each party keeps its own political capital.
Everyone would be better off if Republicans and Democrats collaborated. However, each party rationally selects a strategy (warfare) that leads them away from this outcome. They know that if they prepare for conflict, instead of collaborating, and somehow manage to win the arm wrestling match, they can get 10 points and rob the opposition of 3—and that, in the worst case scenario, there will be a tie (0 points) and they will neither lose nor gain anything. If they collaborate, their winnings are capped at only 7 points (not 10), and, what is worse, if they collaborate and the other party starts a battle, they could suffer a -3 point defeat. Fighting therefore gives each party either 10 points rather than 7 or 0 points rather than -3. So, no matter what the other party does, each party is better off fighting than collaborating.
In this game, the battle strategy is a Nash equilibrium—named after mathematician John Nash, who was portrayed in the film A Beautiful Mind. A Nash equilibrium is a game of simultaneous choices, in which no player can improve his outcome by unilaterally changing his choice (a better equilibrium depends on collaboration).
In our real world political scenario, if we end up with a 0–0 score, neither party would be better off changing its choice: each party would only stand to lose (moving to the -3 square) by changing its individual strategy. The only way to get a better outcome would be to cooperate. But each party cannot be sure that the other party will cooperate. Given this uncertainty (lack of trust), the most rational strategy is to do battle, no matter what the other party does. That is why the political warfare strategy is dominant over the cooperative strategy.
Game 2: Assurance Game (CNN vs. FoX)
The dilemma in Game 1 is that both parties are better off selecting conflict because they can’t be sure the opposition will select cooperation—even though doing battle leaves them both worse off than mutual cooperation would. In order to make both players select cooperation, then, we need a reliable tie. Assurance games model exactly that: scenarios with multiple equilibria, in which moving from a worse equilibrium to a better one requires commitment.
People have long complained that the American media are politically biased. There is widespread public perception that CNN is left-wing, while Fox is right-wing. We can check that assumption by looking at their respective coverage of the Coronavirus crisis: “Trump’s White House in Chaos Over Coronavirus” (CNN); “Top Democrats and Their Media Allies Refuse to Give President Trump Credit for Anything” (Fox).
Both CNN and Fox know that they can continue in this vein and please their most devoted respective audiences, which gives them 20 points each. But, due to this perception of political bias, some people think that the media are becoming less trustworthy. If both channels cooperated, they could broadcast news a little more objectively—avoiding direct attacks. They could make peace with each other and recover credibility (50 points each). However, if only one channel tempers its presentation of the news and the other sticks to its strong opinions, there will be a clear winner: one will gain 20 points for what can be judged as assertiveness and the other only 5 points for what can be misread as apathy.
This is an assurance game with two equilibria: (a) both networks shift to neutrality and moderation (50 points each) or (b) both retain their current political alignments and aggressive behavior (20 points each). If they both found themselves in the square of neutrality, neither would have any incentive to change its choice. However, the same goes for the political involvement square: since both channels are parked there, neither is any better off changing its choice alone. If CNN sticks to political alignment and Fox unilaterally shifts to neutrality, the balance will favor CNN (and the left-wing spectrum)—and vice versa. This situation would not be an equilibrium: whether or not CNN selects propaganda, Fox will never select neutrality, since, by changing its choice, it would be worse off (by 20 points to 5 points).
Assurance games are peculiar because it is possible to find two equilibria points in their payoff matrices. For example, there are two ways to reach a political equilibrium in media coverage: (a) double cooperation towards neutrality; (b) individual, opposing partialities. Still, one of the equilibria seems to be better for both players—double objectivity renders 50 points and double partiality only 20. So why don’t CNN and Fox end up choosing moderation every day?
Players can only choose strategies, not outcomes. Even though both channels would be better off choosing impartiality together, since they make their choices individually, there is no guarantee that the other party will choose the same option. Without strong bonds (trustworthiness), the payoff-dominant strategy in which both select neutrality may not materialize.
Game 3: Repeated Games (Trump vs. Cuomo)
Since some games (like Game 2) have multiple equilibria, it is natural to wonder whether something can be done to move players from an inferior equilibrium to a superior one. One way to do that is to find an equilibrium in which at least one player is better off, and none is worse off. This is called a Pareto improvement, after Italian economist Vilfredo Pareto.
In some games, it is very hard to make players move from a Nash equilibrium to a Pareto optimal equilibrium (see Game 1). But that doesn’t mean that players are always doomed to a suboptimal outcome. There is a variable that can help: repetition, which may provide information that allows players to escape the dilemma and move to a cooperative (and higher) equilibrium.
Fortunately, not all games are isolated one-time situations: we also have repeated games, in which players can reshape their behavior and make new choices based on the past movements of the other player. This is what happened to President Trump and New York governor Andrew Cuomo.
Initially, the two men had a back and forth, in which they expressed strong criticism of each other’s efforts to combat the Coronavirus. Trump said that, “Governor Cuomo should spend less time complaining and get the job done.” Cuomo responded that, “if he [Trump] is sitting home watching TV, maybe he should get up and go to work, right?” After all the finger-pointing, Cuomo changed his mind and declared that the President was “fully engaged” with the crisis and “very creative and energetic.” Trump dropped his usual defences and both were able to put aside their dispute.
This game proceeds as follows. President Trump and Governor Cuomo can be friends or foes: they can “shake hands” (6 points each) or “get into a fistfight” (-1 point each). If one of them reaches out for a handshake while the other attempts to throw a punch, we have a disequilibrium, such that the player who punches can gain an advantage (2 points) and cause damage to the other’s public image (-3 points). There are therefore two possible equilibria: (a) both shake hands; or (b) both come to blows. In this setup, handshaking is clearly a Pareto improvement over punches.
In an isolated game, it is uncertain whether handshaking is the rational strategy, unless the political environment promotes handshaking (it does not) or they can communicate and react in real time (they can’t). As a consequence, even in a game with multiple Nash equilibria, the fact that one Pareto equilibrium is dominant over the other is not enough to guarantee that the players will achieve that equilibrium—causing damage to the opposite player is always a temptation and politicians are typically reluctant to take the risk of being perceived as weak.
How, then, were Trump and Cuomo able to end up cooperating, unlike the Republicans and Democrats of Game 1? The answer lies in the punishment known as tit for tat whereby, in repeated games, players might mirror each other’s actions as punishment.
Since Trump initially selected punches, Cuomo responded with punches, since he couldn’t concede to being hit without responding or he would have received -3 points; both of them were scratched (-1 point). Given that they both have enough problems already, and that the public is fed up with these political disputes in the midst of a health crisis, Cuomo shifted his behavior, predicting that Trump might also be willing to dodge unnecessary quarrels, if possible. Indeed, Trump reciprocated. Cooperation between the two players could then continue in subsequent rounds.
Game 4: Coordination Game (Reopen v.s Shutdown)
Network effects or network externalities are situations in which the utility of a good or service increases when others adopt it. Think about social media. Since Facebook and Twitter have decided to silence anyone who ventures to express ideas that they consider to be wrong, I’d like to create a new social media platform, free from censorship. However, if very few people join my platform, it will be useless. This applies to many political choices.
In this Coronavirus crisis, one key issue is whether the policies adopted by different states are compatible across the US. This presents a potential coordination problem for states: should they adopt a strategy that is compatible with those of the others, everyone benefits; should they adopt conflicting strategies, both sides will lose. We will assume that, by the players’ own lights, both situations of compatibility are equally good: reopen-reopen boosts the economy and shutdown-shutdown helps to flatten the curve.
This situation presents two equal Nash equilibria (4 points): (a) if states reopen, producers, wholesale markets and retailers can interact, such that all of them can increase their economic activity, creating income and employment and offering some relief if the number of fatalities increases; (b) if states remain in lockdown, the economy will suffer, but they can be more confident that the number of sick people will not exceed the capacities of their health services.
If, however, states select different (incompatible) strategies, both sides might get into trouble (-2 points): (a) since many economic sectors rely on travel, the interstate flow of people may lead to a growth in the number of infected everywhere, as people’s comings and goings spread the disease; (b) since the economy is interconnected, if only part of the supply chain reopens, setbacks may slow or even shut down manufacturing, producing shortages that might cause the economic recovery to falter.
Though they may be unaware of the theory, this kind of argument has been used by leaders who want to centralize the management of the crisis and enforce uniform measures to either combat the virus or reopen the economy. In mid April, President Trump claimed “total authority” over states’ decisions, after some had announced regional plans for reopening on their own timelines. Soon afterwards, he unveiled a plan to reopen the economy in phases and granted states broad autonomy. Now, coordination is in the hands of states (a new game emerges).
Game 5: Battle of Preferences (Wisconsin vs. Michigan)
Considering the network effect we saw in Game 4, it is not surprising that states prefer to embrace compatible strategies—several states, including Michigan and Wisconsin, have formed pacts to decide together when to reopen economies. This does not mean that there is a homogeneous consensus. Some states may have preferences: Michigan wants to remain closed, while Wisconsin has already started to reopen.
In this game, Wisconsin receives a better payoff (7 points) if it adopts its preferred strategy and makes Michigan ease lockdown too (3 points). The same is true in the reverse situation: Michigan would be better off (7 points) if Wisconsin could be convinced to sustain the lockdown (3 points). We will use -1 points to indicate a lack of coordination, the least preferred outcome (reopen/shutdown or shutdown/reopen), in which each individual government does what it thinks is best for its citizens, though the incompatible policies hurt both states.
There are two Nash equilibria here. But, unlike in Game 4, these states are not indifferent between the possible equilibria because the payoffs are not the same. Hence, since the players have preferences, regardless of which option is chosen, one state will be less satisfied than the other, even though neither state has an incentive to change its strategy, because it is wary of falling into the wrong diagonal (lack of coordination).
Coordination problems are normally solved through some mechanism that provides guides to actions and interactions, backed by explicit and implicit punishments for deviation, and which therefore allows players to create shared expectations. While formal standards (executive orders) continue to mandate that states maintain lockdowns, this is likely to be the trend—it is not easy to move out of this safety zone. However, once states gradually begin to reopen under public, business or political pressure, the incentives to maintain lockdowns will diminish and sequential choice conditions will push states towards coordination.
Game 6: Sequential Choice Games (Georgia vs. Texas)
Amanda Mull has speculated that “Georgia is reopening amid the coronavirus pandemic” as an “experiment in human sacrifice … to find out how many people need to lose their lives to shore up the economy.” But is that true?
There is a big difference between games that feature simultaneous choices and games that permit sequential choices. In Game 5, states don’t need to make their choices at the same time and the order in which they do so may result in very different outcomes in the medium term. Let’s call this phenomenon following the leader.
Some weeks ago, politicians from Texas and Georgia started to say that maybe it was time for people to get back to work. But, while this might be possible with the cooperation of a couple of other states, it is problematic to open up one your own because that makes you look odd. At the time, no state could be sure that any other state would really resume economic activities. The fear of being the only one to reopen, and therefore labeled an irresponsible outlier, led states to exercise caution and wait a little longer. Then, despite not having met the benchmarks set by the White House in its reopening guidelines, Georgia moved into phase one. Thereafter, several other states, including Texas, began to lift their lockdowns. Why? Look at the payoff matrix below.
In a simultaneous choice game, risk aversion and uncertainty may drive all players to inertia—both states remain closed (neutral = 0 points) rather than risk being the exclusive target of media outrage (-5 points). If Georgia opens and Texas remains closed, Texas can gain an advantage from watching the reaction to Georgia’s reopening and evaluate the political climate (2 points). If the situation is reversed, the points are reserved as well.
In a game of sequential choices, however, there is one additional important detail: subsequent players can follow the leader (9 points each). If an outcome is believed to be the best outcome for everyone and the only thing preventing players from achieving that outcome is reluctance to take steps towards it unaccompanied, once the first player (the leader) makes a movement towards the preferred outcome, subsequent players can follow suit. That explains why Georgia might have begun a new trend.
Upgrading to Pareto Improvements
Game theory helps us understand decisions that seem irrational and even indefensible, without rushing to moral judgements. We should not defend the indefensible, but we can disclose the rationality within the apparent irrationality and, equipped with this knowledge, work to ascend to higher equilibria in our challenging political games.
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“Everyone would be better off if Republicans and Democrats collaborated. However, each party rationally selects a strategy (warfare) that leads them away from this outcome.” Interesting. Does this mean that “game theory” presupposes a zero-sum partisan basis for politics (i.e., like football, if they score, we lose). That certainly seems to explain present US politics, but is it necessary? Is it possible that two or more parties might see themselves as advocating different strategies for reaching the same goal (i.e., our differences are real but we are all on the same team in terms of the ultimate objectives — fair, secure, harmonious society, etc.)? Can game theory account for a game in which players are all on the same team but stake out different strategies for advancing team interests? Or is the warfare/battle paradigm built into game theory?