# The role of aggregate information in a binary threshold game

- 12 Downloads

## Abstract

We analyze the problem of coordination failure in the presence of imperfect information in the context of a binary-action sequential game with a tipping point. An information structure summarizes what each agent can observe before making her decision. Focusing on information structures where only “aggregate information” from past history can be observed, we characterize information structures that can lead to various (efficient and inefficient) Nash equilibria. When individual decision making can be rationalized using a process of iterative dominance (Moulin, Econometrica 47:1337–1351, 1979), we derive a necessary and sufficient condition on information structures under which a unique and efficient dominance solvable equilibrium outcome is obtained. Our results suggest that if sufficient (and not necessarily perfect) information is available, coordination failure can be overcome without centralized intervention.

## References

- Azrieli Y, Levin D (2011) Dominance-solvable common-value large auctions. Games Econ Behav 73:301–309CrossRefGoogle Scholar
- Basu K, Pattanaik P (2014) Nash equilibria of games when players’ preferences are quasi-transitive. MimeoGoogle Scholar
- Ben-Porath E, Dekel E (1992) Signaling future actions and the potential for sacrifice. J Econ Theory 57:36–51CrossRefGoogle Scholar
- Brandenburger A, Friedenberg A, Keisler HJ (2008) Admissibility in games. Econometrica 76:307–352CrossRefGoogle Scholar
- Chwe MS-Y (2000) Communication and coordination in social networks. Rev Econ Stud 67:1–16CrossRefGoogle Scholar
- Chwe MS-Y (2001) Rational ritual: culture, coordination, and common knowledge. Princeton University Press, PrincetonGoogle Scholar
- Dawes RM, Orbell JM, Simmons RT, Van de Kragt A (1986) Organizing groups for collective action. Am Polit Sci Rev 80(4):1171–1185CrossRefGoogle Scholar
- Ewerhart C (2000) Chess-like games are dominance-solvable in at most two steps. Games Econ Behav 33:41–47CrossRefGoogle Scholar
- Ewerhart C (2002) Iterated weak dominance in strictly competitive games of perfect information. J Econ Theory 107:474–482CrossRefGoogle Scholar
- Galeotti A, Goyal S, Jackson MO, Vega-Redondo E, Yariv L (2010) Network games. Rev Econ Stud 77:218–244CrossRefGoogle Scholar
- Glaeser EL, Sacerdote B, Scheinkman JA (1996) Crime and social interactions. Q J Econ 111:507–548CrossRefGoogle Scholar
- Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83:1420–1443CrossRefGoogle Scholar
- Gretlein R (1982) Dominance solvable voting schemes: a comment. Econometrica 50:527–528CrossRefGoogle Scholar
- Hammond P (1976) Equity Arrow’s conditions, and Rawls’ difference principle. Econometrica 44:793–804CrossRefGoogle Scholar
- Kreps D, Wilson R (1982) Sequential equilibria. Econometrica 50:863–894CrossRefGoogle Scholar
- Kohlberg E, Mertens JF (1986) On the strategic stability of equilibria. Econometrica 54:1003–1037CrossRefGoogle Scholar
- Koriyama Y, Núñez M (2015) How proper is the dominance-solvable outcome? MimeoGoogle Scholar
- Mailath G, Samuelson L, Swinkels J (1993) Extensive form reasoning in normal form games. Econometrica 61:273–302CrossRefGoogle Scholar
- Marx L, Swinkels L (1997) Order independence for iterated weak dominance. Games Econ Behav 18:219–245CrossRefGoogle Scholar
- Milgrom P, Roberts J (1990) Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58:1255–1277CrossRefGoogle Scholar
- Moulin H (1979) Dominance solvable voting schemes. Econometrica 47:1337–1351CrossRefGoogle Scholar
- Moulin H (1986) Game Theory for the Social Sciences, 2nd edn. New York University Press, New YorkGoogle Scholar
- Osborne MJ, Rubinstein A (1994) A course in game theory. MIT Press, CambridgeGoogle Scholar
- Rochet JC (1980) Selection of a unique equilibrium payoff for extensive games with perfect information. D. P. CEREMADE, Université Paris IXGoogle Scholar
- Samuelson L (1992) Dominated strategies and common knowledge. Games Econ Behav 4:284–313CrossRefGoogle Scholar
- Satterthwaite M, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48:587–97CrossRefGoogle Scholar
- Sen A (1977) On weights and measures: informational constraints in social welfare analysis. Econometrica 45:1539–1572CrossRefGoogle Scholar
- Schelling T (1969) Models of segregation. Am Econ Rev 59:488–493Google Scholar
- Schelling T (1973) Hockey helmets, concealed weapons, and daylight saving: a study of binary choices with externalities. J Confl Resolut 17:381–428CrossRefGoogle Scholar
- Tyson C (2010) Dominance solvability of dynamic bargaining games. Econ Theory 43:457–477CrossRefGoogle Scholar
- Watts D (2002) A simple model of global cascades on random networks. Proc Natl Acad Sci USA 99:5766–5771CrossRefGoogle Scholar