Games superheroes play: Teaching game theory with comic book favorites

ABSTRACT

The valuable insights of game theory sometimes remain out of reach for students who are overwhelmed by the subject's complexity. Comic book applications of game theory, with superheroes as players, can facilitate enthusiasm and classroom interaction to enhance the learning of game theory. Drawing from content in superhero movies and books, the authors construct games to illustrate pure-strategy Nash equilibrium, Bayes-Nash equilibrium, mixed strategies, sub-game perfection, and perfect Bayesian equilibrium. To help instructors build students' skills in finding and interpreting game solutions, they translate comic book scenarios into specific game forms; however, not all scenarios are obvious so they suggest instructors help students develop their own game-theoretic judgments to determine what game forms, payoffs, and solution concepts might be appropriate for understanding a situation.

KEYWORDS:

• cartoons
• comics
• economic education
• game theory
• superheroes

JEL CODES:

• A12
• A22
• C70
• Z11

Acknowledgments

The authors thank William C. Wood for constructive comments. They appreciate the help of Jason Jackman, comic book fan, Dave the comic book guy at Big Bang Comics and Collectibles in Sewickley, Pennsylvania, and the staff of the Comics Dungeon in Seattle, Washington, for their recommendations. They are also grateful for the feedback from three referees.

Notes

1. Some might go back as far as 1989 when the relaunch of the Batman franchise began. However, the premiere of the X-Men launched a small frenzy of superhero based films. In 2002 Spider-Man appeared in theaters followed in 2003 by Daredevil, The Hulk, and X-Men 2.

2. In the movie, the main combatants include Captain America, Hawkeye, Falcon, Bucky Barnes, Scarlet Witch and Ant-Man squaring off against Iron Man, War Machine, Black Widow, Black Panther, The Vision and Spider-Man. The comic book version of this story involves many other heroes and different alliances (Miller 2007).

3. Of course, one of Batman's rules of engagement is that he will not kill, so Joker may have been banking on this information.

4. Hero-villain team ups happen quite a bit in the comics. Superman and Lex Luthor, Batman and Joker, Spider-Man and Venom, Dr. Doom and Dr. Strange are just some examples.

5. Batman has a picture of his Bat-family in the Batcave in The Killing Joke. Among the people in the picture is Batwoman. Alas, there is no picture of Commissioner Gordon.

6. This game and its solution are similar to the Air Strike game in Osborne and Rubinstein (1994).

7. The answers reflect propositions found in Osborne's introductory game theory textbook (2004, 116):

A mixed strategy profile α^* in a strategic game with vNM preferences in which each player has finitely many actions is a mixed strategy Nash equilibrium if and only if, for each player i,

• the expected payoff, given α_−i^*, to every action to which α_i^* assigns positive probability is the same.

• the expected payoff, given α_−i^*, to every action to which α_i^* assigns zero probability is at most the expected payoff to any action to which α_i^* assigns positive probability.

8. A different interpretation of such a hostage situation could involve a lower payoff for the hero from the hostage-no-kill apprehension outcome than from the no-hostage outcome. Such an alternative interpretation would reflect the idea that the nonlethal trauma inflicted on the hostage outweighs the advantage in apprehending the villain.