Game Theory of Political Negotiation

This is a more analytical approach to my post on the Dinner Bargain of 1790 that depicted the drama between Secretary of Treasury Hamilton and his political rivals over proposals to resolve state war debts and set up a national bank. Check out that post for a refresher on the story!

This piece will look at the bargaining process between the Federalists, led by Alexander Hamilton, and anti-Federalist coalition, from a game theory perspective. There are several aspects to consider:

Game Design

Human conflict is very complex to predict but game theory can be a useful tool to glean insights into the thought process of the Founding Fathers as they went through the negotiation process. It’s a high impact game and the course of the young republic were tied to the outcome. Game theory applies math to think through how the situation evolves based on strategic interactions between the players.

On one side, there’s Hamilton who is the standard-bearer for Federalists, advocating for the federal government to exert a strong influence on economics and politics. On the other end, Madison and Jefferson represent the coalition of anti-federalists and the Southern bloc who believe power resides with states. Jefferson, a wealthy land-owner who believes in a pastoral America, wants to delay government intervention even facing a fiscal crisis.

Chicken Game

The Chicken dilemma game is one type of game that illustrates the showdown between Hamilton and his opposition. It’s like a modern-day version of political logrolling or horse trade. In Chicken, each player has two strategies: swerve or go straight. Each play does not have a dominating strategy, unlike a prisoner’s dilemma game. Each player adopts a counter-coordination strategy against the opponent. If the Player 2 swerves, then Player 1 would go straight. If Player 2 goes straight, then Player 1 would swerve. Each player is testing each other’s patience and stays resolve until the other player gives up and back out.

When each player enacts their optimal strategy given the strategy taken by the other player, this is referred to as a Nash equilibrium. In the chicken game, there are two pure strategy Nash equilibria:

  1. Player 1 goes straight and P2 swerves. The payoff matrix results in +1 for Player 1 since she stayed strong and -1 for Player 2 since he backs out. 
  2. Player 2 goes straight and Player 1 swerves. There’s an incentive for a player to continue straight while the other player swerves. In a mirror outcome, the payoff matrix results in +1 for Player 2 since he stayed strong and -1 for Player 1 since she could not stomach it.  

But suppose the two scenarios above don’t happen, then it’s possible both players would swerve. If both don’t swerve, then both continue straight and ultimately collide. The worst payoff results from the two players running straight at each other. 

A strategy where both players go straight, both players have an incentive to change strategy given it’s the worst outcome for both players. If collectively choose to keep going, one would switch strategy by swerving, for example player 2 swerve because 0 is better than negative utility if gone straight. Player 1 has an incentive to change strategy to swerve. Keep going and Keep going will not be played strategy in a pure strategy Nash equilibrium. If P1 goes straight and P2 swerves, P2 doesn’t have an incentive to change strategy by going straight because it would yield a negative utility of -5.

What exactly is a Nash Equilibrium then? For a player, this entails a set of strategies such that the player has no incentive to change strategy given what the other players are doing. Although we know someone will swerve, but we may not know which one will serve in a Chicken Game. However, in reality, we know Hamilton had more interests in cooperating or making bargains in order to get his economic proposals approved by Congress.

Just like in the standard Chicken design, there are two pure strategy Nash equilibria in this game:

(1) Federalist swerve and Anti-federalist goes straight; 

(2) Anti-federalist goes swerve while Federalists go straight. It’s an anti-coordination game.

Mutual defects by both parties would be disastrous for America already in shaky conditions. Since Founding Fathers were statesmen who believe in moving the country forward,  it’s better for a player to swerve (i.e. cooperate) rather than all players defect. Applying chicken to the debate among our Founding Fathers, it’s a classic Congressional gridlock.  It’s mutually beneficial for the Federalists and anti-Federalists to adopt different strategies. Federalists wanted a strong government and preemptive federal assumption of state government debt. Anti-federalists rather the federal government disappear from the picture even amidst the crisis. Madison led the Southern state coalition, wanted to pass the Permanent Residence Bill to establish permanent Federal Government and national capital outside of Virginia. Hamilton, “Federalist coalition”, wanted to pass the Funding bill allowing the federal government to assume state debt. 

This is a repeated game since policy debates and negotiations are ongoing even before the 1790 Bargain. Each side has reputational incentive to win/lose. The ultimate loser is the U.S. economy and possibly its ability to forge ahead as a new country under acute fragile economic conditions and fractured leadership. Breaking the gridlock was Secretary of State Jefferson who set up a dinner between Madison and Hamilton to knock out a bargain. 

The game of chicken has played out over the course of history between presidents and Congress. In recent history, to force the other side to accept a downsized government budget, President Reagan ordered the suspension of government services which impacted 800,000 federal employees. That same day the U.S. Congress resolved the situation by approving funding of the government.

Decades later in 1995, President Bill Clinton and his Treasury Secretary Robert Rubin had a record showdown against Congressional Republicans. Congressional leaders opposed the President’s offer to keep the government open during the negotiation. During President Barack Obama’s showdown with Republican leaders in Congress, the government also temporarily laid off 800,000 federal employees.

Prisoner’s Dilemma

Rather than the Chicken Game, we can dissect the political negotiation process using a slightly different game design known as the Prisoner’s Dilemma (PD). Suppose two criminals from Al Capone’s gang are caught. Each are seated in a separate room. This is a single game with no communication between the two players. The FBI offers each a choice: either rat out the gang or stay silent. By design, this is a non-cooperative game with dominant strategies where each player has a preferred strategy. The dominant strategy for each player is to defect since it gives the highest payoff regardless of what the other player does. 

Player 1’s preferred strategy is to defect, ratting out the gang first since he wants a reduced sentence, thinking that the other guy will likely rat out the gang anyways. Player 2’s preferred strategy is to defect. When both guys rat out the gang, they indict the entire gang. So both players’s default strategy is to defect given what the other player is doing in the holding room. The expected outcome of Prisoner’s Dilemma is defect-defect or otherwise known as the Nash Equilibrium. However, it’s a Pareto suboptimal outcome–not an ideal result. The optimal outcome would be both players cooperating by staying silent so the police can’t indict anyone. Collectively that would be an efficient result but individual preferred strategy leads them astray.

Whether it’s the Chicken Game or the Prisoner’s Dilemma, there is a broader takeaway for U.S. economic policy. We already saw the dynamics between Hamilton and Madison are similar to modern fiscal showdowns in Congress with the decision of whether to approve the budget to keep the government open or shutdown government services. It’s clear that by Constitutional design, separation of power between the Executive Branch and Congress, as well as checks and balances between political parties, can lead to brinkmanship. This phenomenon is secular to the party in power or political affiliation of the US President. 

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