RULE RATIONALITY

• Author: Eyal Winter,Yuval Heller
• DOI: http://doi.org/10.1111/iere.12183
• Published date: 01 August 2016
• Date: 01 August 2016

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 3, August 2016

RULE RATIONALITY∗

BYYUVAL HELLER AND EYAL WINTER1

University of Oxford, U.K; Hebrew University of Jerusalem, Israel

We study the strategic advantages of following rules of thumb that bundle different games together (called rule

rationality) when this may be observed by one’s opponent. We present a model in which the strategic environment

determines which kind of rule rationality is adopted by the players. We apply the model to characterize the induced

rules and outcomes in various interesting environments. Finally, we show the close relations between act rationality

and “Stackelberg stability” (no player can earn from playing first).

1. INTRODUCTION

Act rationality is the notion that perfectly rational agents choose actions that maximize

their utility in every specific situation. However, both introspection and experimental evidence

suggest that people behave differently and follow “rule rationality”: They adopt rules of thumb,

or modes of behavior, that maximize some measure of average utility taken over the set of

decision situations to which that rule applies; then, when making a decision, they choose an

action that accords with the rule they have adopted. As a result of bundling together many

decision situations, this rule of thumb induces smaller cognitive costs and fewer informational

requirements (see Baumol and Quandt, 1964; Harsanyi, 1977; Ellison and Fudenberg, 1993;

Aumann, 2008, and the references there in).

Reducing the cognitive costs is arguably the main advantage of such rules of thumb, but

it is not the only advantage. Rule-rational behavior can also arise from religious, moral, or

ideological rules, which are unrelated to cognitive limitations. Such rules allow players to

commit to a certain behavior and by that affect the behavior of others to their advantage. For

example, the Jewish rules of a kosher diet serve as an important commitment device. As eating

together is an important social event, such dietary restrictions serve as a credible commitment

to refrain from major social interaction with non-Jews and hence a commitment to engage

socially within the community. A rule that bans eating with non-Jews would have been too

stringent and too costly and would not have been able to survive. Likewise, when a state or a

military organization chooses to follow the Geneva conventions regarding prisoners of war, it

establishes a commitment that binds the incentives of the enemy to fight to the “last drop of

blood.” Politeness rules such as “ladies first” facilitate coordination.

In all these as well as similar examples, bounded cognition is of little relevance, and emotions,

moral standards, and social norms dictate the rule. The role of commitment in strategic situations

has been extensively investigated since the seminal work of Schelling (1960; see, e.g., Bade et al.,

2009; Renou, 2009; and the references within for recent papers in this vast literature). Although

commitment has always been studied in the context of a single game, its relationship to rule

behavior in environments of multiple games/situations has not been studied. We believe that

∗Manuscript received October 2014; revised April 2015.

1Eyal Winter is grateful to the German Israeli Foundation for Scientific Research and to Google for their financial

support. Both authors are grateful to the very useful comments of the editor and the referees and to helpful discussion

with the audiences at Queen Mary spring theory workshop and in seminars in Oxford and HUJI.

Please address correspondence to: Eyal Winter, Center for the Study of Rationality and Department of Economics,

Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905 Israel. E-mail: mseyal@mscc.huji.ac.il.

997

C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

998 HELLER AND WINTER

this relationship can shed light on a variety of social rules with which complexity and cognitive

limitation has little to do.

In this article we focus on rule rational behavior in which players bundle games together

while interacting with others who gradually learn the structure of bundling (which allows the

bundling to serve as a commitment device.)2The main contribution of this article is threefold:

(1) We present a tractable model in which the properties of the strategic environment determine

which kind of rule rationality is adopted by the players;(2) we characterize the induced rules and

outcomes in various interesting environments; and (3) we show the close relations between act

rationality and “Stackelberg stability” (no player can earn from playing before his opponent),

and relate it to the value of information.

The extent to which the commitment to act according to a moral or ideological principle is

credible depends on comparing the cost of adhering to the principle relative to the cost of losing

the commitment benefits in the future. These are the kind of considerations we employ in our

model to define rule rationality. The declaration of such principles can be viewed as a signal

that facilitates the gradual learning about one’s bundling strategy by others. To be sure, these

signals are not fully revealing, but the fact that these declarations are very often made and often

taken seriously suggests that stressing ideological or moral principles is not merely cheap talk

either. Roth et al. (1991) demonstrate that a commitment to a principle or a moral standard

becomes a social norm that people act upon.3In the presence of some pre-play communication,

people who contemplate deviating from the social norm (i.e., choosing a different partition)

will use deception, which might be detected by the opponent.4

Another form of rule rationality relevant to our context includes firms or organizations that

adopt rigid policies applying to a broad class of circumstances without elaborating the rationale

of each policy. If a craftsman rejects an offer to accept 50% of his proposed price for doing

50% of the job on the basis that it is “unprofessional” or when a chain store rejects a returned

item after the refund deadline even under exceptional circumstances by simply arguing that “it

is against our policy,” they act within this form of rule rationality.

We now briefly present our model. An environment is a finite set of two-player normal-

form games that share the same set of feasible actions.5The environment is endowed with a

function that determines the probability of each game being played. Each environment induces

the following two-stage meta-game: At stage 1, each player chooses a partition over the set of

games; At stage 2, each player chooses an action after observing the element of his partition

that includes the realized game and his opponent’s partition. A rule-rational equilibrium of the

environment is defined as a subgame-perfect equilibrium of the meta-game. We interpret such

an equilibrium as a stable outcome of a dynamic process of social learning, in which the choices

of partitions in the first stage (interpreted as rules of thumb that bundle games together) and

the behaviors in the second stage (given the partitions) evolve.

A rule-rational equilibrium is act-rational if players always use the finest partition and play a

Nash equilibrium in all games, and it is non-act-rational if at least one of the players does not

best reply in at least one game. The observability of the opponent’s partition is a key assumption

in our model. If the opponent’s partition is completely unobservable, then one can show that

all environments only admit act-rational equilibria. Many of our results can be extended to a

setup of partial observability, and this is discussed in Section 8.2.

2This “commitment” advantage of rule rationality might be of importance also in single-player games as a “self-

commitment” device with a multiple-selves interpretation.

3Roth et al. (1991) study the ultimatum game across different cultures. They find that responders always reject offers

below a certain threshold and that these thresholds are culture dependent (e.g., they are substantially lower in Israel

and Japan than in Slovenia and the United States). Proposers seem to be familiar with the distribution of the threshold

within their own culture.

4See, for example, the findings of Israel et al. (2014), which suggest that watching 30 seconds of pre-play communi-

cation is enough to predict players’ choices better than a random guess.

5Assuming a fixed set of action is without loss of generality; see Footnotes 8 and 11.