Examining Theories of Distributive Justice with an Asymmetric Public Goods Game

Abstract

In this article, the author presents an asymmetric version of the familiar public goods classroom experiment, in which some players are given more tokens to invest than others, and players collectively decide whether to divide the return to the group investment asymmetrically as well. The asymmetry between players raises normative issues about fairness, rights, and equality that are not present in the symmetric game, where efficiency is the major relevant normative concept. Playing the game in class requires students to confront the distributional question and shows how issues of efficiency can become entangled with other moral issues when solving economic policy problems. The game allows instructors to incorporate theories of distributive justice into economic reasoning in the classroom, as has been widely suggested recently.

Keywords:

• classroom experiment
• distribution
• equality
• fairness
• normative economics

JEL codes:

• A2
• B4
• D3
• H4

Notes

¹The call has been prominently presented by Sandel (2012, 2013). Atkinson (2011) and Bhagwati (2011) emphasized the importance of teaching normative welfare economics, and Barrera (2003) proposed several methods for incorporating normative analysis into the curriculum. Several introductory economics textbooks now contain normative material; see (among others) Bade and Parkin (2007) or Colander (2008). Hennessey (2013) discussed teaching normative economics in public finance.

²This game has a long history in economics: Brock (1991) is a relatively early presentation of it, and Holt and Laury (1997) helped popularize it. Holt (1999) discussed the development of classroom games as a pedagogical technique. Stodder (1998) discussed ethical issues in classroom games and in their use.

³Asymmetric voluntary contributions games have been studied for research purposes by Keser et al. (2011).

⁴The public goods aspect of the game is not necessary to the normative point; the same issues could be raised in a game involving redistribution of private goods. However, the group investment feature of the public goods game offers a simple and natural channel by which players can collectively alter the distribution of payoffs, and the public goods game is already familiar to many instructors.

⁵One can introduce bargaining over the division of the group return into the standard game as well. However, in that game, because the students have identical roles in the game, equal division of the group return is the obvious division. The bargaining problem is more interesting in the asymmetric game because equal division is not so focal in it.

⁶I have the students play for purely hypothetical stakes, but one can convert the payoffs to small amounts of real currency and pay the students, or pay one randomly selected student, or offer extra credit points, or do other things that give an explicit incentive to the students to maximize their payoff.

⁷As long as the payoffs of the game represent the player's order of preference among the outcomes, as is standard in game theory, players should always pursue what gives them the highest payoff, regardless of how other players perform. However, players may instead view the payoffs as if they were income or status levels, in which case they may be concerned about having a higher payoff than other players, rather than the highest payoff they can achieve. Although I have not had problems with this in my experience with the game, it has been known to occur in other games. Instructors should be prepared to explain what payoffs mean and tell players to make decisions that maximize their own payoffs without regard to those of others. Instructors who provide tangible incentives for receiving high payoffs may be less likely to have problems with this.

⁸Dworkin (1981) recognized that this can, in effect, compel those born with talents to use their talents in the way that produces the most income, to pay their taxes, even if they would prefer to use them in another way. This problem, known as the “slavery of the talented,” does not occur in the game, and so I do not discuss it here.

⁹Alternatively, one can assume that payoffs represent utility levels directly so that what matters is making the sum of utilities as high as possible. If so, then any point on the payoff frontier is equally good because they all produce a total utility of forty-eight. Any distribution of the payoff is equally acceptable because utilitarianism concerns itself only with the total utility of society and not with the distribution of that utility.

¹⁰Sometimes players propose (31,17) to make the fortunate strictly better off, which does not affect the essential argument that they make.

¹¹Gauthier's solution to the normative problem corresponds to the Kalai-Smorodinsky solution to the bargaining game. A formal derivation of both this solution and the Rawls solution is available from the author on request.