Simulating the Bargaining Model of War

Dr. Kyle Hanes is our guest contributor this week.  An assistant professor of political science at Purdue University, he describes a game he created to simulate the bargaining model of war.  Full instructions on his simulation can be found in his October 2015 PS: Political Science & Politics article.

The bargaining model of war has become so central to scholarly work on interstate conflict that, I would argue, it should be incorporated into even introductory IR courses. The bargaining model’s logic is intuitive and compelling, but even treatments of it in introductory textbooks rely on formal notation that can confuse or alienate many students. I can still hear the crickets echoing through my classroom as I excitedly asked students to explain why “State B will accept any offer greater than 1 – p – c.”

In trying to cut through this notation to explain the bargaining logic and “incentives to misrepresent,” I would often fall back on the logic of gambling. Misrepresentation is, in effect, bluffing. And even if most students don’t host a weekly card game, the majority are at least vaguely familiar with the logic of bluffing in poker. Why does a poker player make a large bet with a weak hand? Doing so might allow them to win the pot without even having to show their cards. Ultimately, it’s the same reason why states exaggerate their military power or willingness to fight over a disputed piece of territory. Over time, I developed this metaphor into a simple, in-class card game that illustrates the core logic of the bargaining model of war. The game is fun, simple, and engages students directly in the bargaining logic. The game’s rules and parameters are extremely flexible, and can be adapted to highlight different components of the bargaining model’s logic.

Students are divided into pairs and are each given a number of poker chips and deck of cards. In each hand, students “ante up” a certain number of chips and deal out a set number of cards. In the first round, all cards are dealt face down so each player knows their own hand, but neither knows anything about their opponent’s. Player 1 (P1) first decides whether to make a demand for the pot – either because they have a strong hand, or because they want to bluff for it. If P1 opts not to make a demand, Player 2 (P2) takes the pot. If P1 does make a demand, P2 must respond by either conceding or resisting. If P2 concedes, P1 takes the pot. If P2 resists, both players turn over their cards, and the player with the highest total card value wins the pot. But crucially, if the winner is determined by flipping over their cards, both players lose a certain number of chips, which are simply removed from the game.

These lost chips represent the “costs of conflict” if players fail to agree on who will take the pot. This captures the bargaining model’s core assumption that fighting is an “inefficient” means of settling disputes. Regardless of which player win the pot after the cards are turned over, both would have been better off if they had agreed to this outcome during the prior bargaining process.

After a predetermined number of hands are played, the game proceeds to the next round. The rules and game play are essentially the same, with one important exception. In each subsequent round an increasing number of cards are dealt face-up, so more of each player’s hand become common knowledge. For example, if in Round 1 each student is dealt three cards face-down, in Round 2 they are each dealt two cards face-down and one card face-up. In Round 3 they are dealt two cards face-up and one card face-down, and so on. In short, each round gives the players more information about their opponent’s bargaining strength.

At the end of each round, the instructor should take note of how many chips were removed from the game for each pair of students. When all rounds are done, the instructor can quickly determine the average number of chips removed from the game per student-pair across each round.

According to the bargaining model’s logic, more information about an adversary’s strength should result in less conflict. In the game, this would mean that when more cards are dealt face up, students should be more likely to agree on who should take the pot without having to turn their cards over. For instance, if P1 is showing an ace and P2 has all low cards, P2 knows for certain that conceding to P1’s demand would yield the highest payoff. Even limited amounts of information can thus decrease the likelihood of bargaining failure. Compiling and presenting aggregate results can illustrate the general point about information and conflict.

But asking students to explain the thought process underlying their decisions, especially in anomalous pairings, can be particularly enlightening. Some students, for example, will make or resist demands simply out of spite. Others will do so in an attempt to establish reputations for toughness. Such outcomes are excellent opportunities to highlight the flexibility and limitations of the bargaining model’s rationalist assumptions.

As mentioned above, and as described in greater detail in my article, instructors can adjust the game’s parameters to highlight different components of the bargaining model’s logic. For example, increasing the number of chips removed from the game as a result of bargaining failure can simulate more costly conflict. Allowing players to “split the pot” can simulate greater “issue divisibility.” Both should make conflict less likely.

The simulation described above is a simple, intuitive way to help students actively engage the logic bargaining, misrepresentation, and costly conflict. The game is extremely adaptable and does not require an enormous amount of preparation or explanation. And perhaps most importantly, it doesn’t require instructors to utter the phrase “one minus p minus c” in an intro IR classroom.