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Erschienen in: Dynamic Games and Applications 4/2021

21.04.2021

Privacy, Patience, and Protection

verfasst von: Ronen Gradwohl, Rann Smorodinsky

Erschienen in: Dynamic Games and Applications | Ausgabe 4/2021

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Abstract

We analyze repeated games in which players have private information about their levels of patience and in which they would like to maintain the privacy of this information vis-à-vis third parties. We show that privacy protection in the form of shielding players’ actions from outside observers is harmful, as it limits and sometimes eliminates the possibility of attaining Pareto-optimal payoffs.
Vorheriger Artikel Asymmetric Partisan Voter Turnout Games
Nächster Artikel Some Game-Theoretic Remarks on Two-Player Generalized Cops and Robbers Games

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Fußnoten
1
Such an association is corroborated by surveys of individuals’ privacy concerns, such as Rainie et al. [46] and Madden et al. [36].
 
2
Loosely, a mechanism satisfies \(\varepsilon \)-DP for some individual i if the distribution over the outcomes of the mechanism with i present is \(\varepsilon \)-close to the distribution with i absent [16]. See Dwork [17] for a survey and Abowd and Schmutte [1] for a discussion of DP from an economic point of view.
 
3
This is captured by the celebrated folk theorem—see, for example, Theorem 13.17 of Maschler et al. [39].
 
4
See Sect. 5 for a discussion of this assumption on the extreme nature of patience and impatience.
 
5
This future game may take the form of a bargaining game, à la Rubinstein [49], in which case they would have an advantage if they were to be perceived as patient. Alternatively, the future game could take the form of the buyer–seller bargaining model of Fudenberg and Tirole [22], where, in equilibrium, impatient buyers obtain the goods at lower prices. Given the ambiguity of the future interaction, the buyers would rather not have their type revealed in the current game.
 
6
Section 4 is significantly longer and more complex than Sect. 3, as the latter is a possibility result that involves an equilibrium construction, whereas the former is an impossibility result that shows that no equilibrium attains particular Pareto-optimal outcomes.
 
7
As an example of nonexistence, suppose payoffs consist of a sequence of \(10^k\) 0’s, then \(10^{k+1}\) 1’s, then \(10^{k+2}\) 0’s, and so on. In this case the \(\liminf \) is 0 whereas the \(\limsup \) is 1, and so the limit does not exist.
 
8
If we consider payoffs at a random period, then when there is a finite horizon this would equal the mean payoff. A natural extension of this criterion to the game with an infinite horizon is the limit of the finite horizon means, as we propose.
 
9
We will assume that the long-sighted player incurs a disutility that depends on the prior and the belief after the repeated interaction. The short-sighted player can be modeled in one of two ways: either he also incurs a disutility that depends on the prior and on the belief after the repeated interaction, or he incurs a disutility that depends on the beliefs before and after each stage. We will adopt the latter for simplicity; using the former, however, would not alter our results.
 
10
The short-sighted type may incur costs at each stage, and so we do not require his costs to be nonnegative to avoid dynamic inconsistency (see [30], for discussion).
 
11
The existence of the expectations for the costs is guaranteed by the boundedness of \(c_i\)—see, for example, Theorem 4 of Royden and Fitzpatrick [48].
 
12
Long-run payoffs in our model are the limit-of-means of stage games, and so on the same order of magnitude, but our results would be unchanged if the long-run payoffs were a large multiplicative factor of the limit-of-means, in which case the privacy cost would be small when compared with the long-run payoffs.
 
13
These are needed for Lemma 4 and consequently one claim of Theorem 2. For any game, they hold with probability 1 following a perturbation of the utilities.
 
14
An alternative definition is \(\mathrm {PF}=\{v\in V^*: \not \exists v'\in V^*~\text{ s.t. }~v'> v\}\) (the difference is in the inequality). If \(V^*\) is a rectangle, for example, then the question is whether the top and right segments are part of \(\mathrm {PF}\) or just the top right vertex. The choice of definition does not matter for our results.
 
15
The symmetry and genericity assumptions in the second bullet are necessary for our proof (in particular, for the proof of Lemma 4), but we do not know if they are necessary for the result to hold.
 
16
Recall that the limit exists with probability 1 by Definition 1.
 
17
See the proof of Proposition 5 in Fudenberg et al. [21] for details and definitions of \(I_t\) and \(m^i\).
 
18
Note that the cases are not mutually exclusive, and that the latter two would suffice. We include the first for illustrative purposes and because it involves a shorter revelation phase.
 
Literatur
1.
Abowd JM, Schmutte IM (2019) An economic analysis of privacy protection and statistical accuracy as social choices. Am Econ Rev 109:171–202 CrossRef
2.
Acquisti A, Taylor CR, Wagman L (2016) The economics of privacy. J Econ Lit 54:442–492 CrossRef
3.
Ali SN, Bénabou R (2020) Image versus information: changing societal norms and optimal privacy. Am Econ J: Microecon 12(3):116–164
4.
5.
Aumann RJ, Maschler M, Stearns RE (1995) Repeated games with incomplete information. MIT press, Cambridge
6.
7.
Becker GS (1974) A theory of social interactions. J Polit Econ 82(6):1063–1093
8.
Benabou R, Tirole J (2006) Incentives and prosocial behavior. Am Econ Rev 96(5):1652–1678 CrossRef
9.
Bergemann D, Hörner J (2018) Should first-price auctions be transparent? Am Econ J: Microecon 10:177–218
10.
Bernheim BD (1994) A theory of conformity. J Polit Econ 102(5):841–877 CrossRef
11.
Calzolari G, Pavan A (2006) On the optimality of privacy in sequential contracting. J Econ Theory 130:168–204 MathSciNetCrossRef
12.
Chaves IN (2019) Privacy in bargaining: the case of endogenous entry. Available at SSRN 3420766
13.
Chen Y, Chong S, Kash IA, Moran T, Vadhan S (2013) Truthful mechanisms for agents that value privacy. In: Proceedings of the fourteenth ACM conference on Electronic commerce. ACM, pp 215–232
14.
Chen Y, Sheffet O, Vadhan S (2014) Privacy games. Web and internet economics. Springer, Newyork, pp 371–385 CrossRef
15.
16.
Dinur I, Nissim K (2003) Revealing information while preserving privacy. In: Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, pp 202–210
17.
Dwork C (2008) Differential privacy: a survey of results. International conference on theory and applications of models of computation. Springer, Newyork, pp 1–19
18.
Dwork C, Nissim K (2004) Privacy-preserving datamining on vertically partitioned databases. Annual international cryptology conference. Springer, Newyork, pp 528–544
19.
Dwork C, Smith A (2010) Differential privacy for statistics: what we know and what we want to learn. J Priv Confid 1:2
20.
Friedrichsen J (2013) Signals sell: designing a product line when consumers have social image concerns. Tech. rep., Discussion paper, Social Science Research Center Berlin (WZB), Research area markets and choice, research unit market behavior
21.
Fudenberg D, Kreps DM, Maskin ES (1990) Repeated games with long-run and short-run players. Rev Econ Stud 57:555–573 MathSciNetCrossRef
22.
23.
Fudenberg D, Villas-Boas JM (2006) Behavior-based price discrimination and customer recognition. Handb Econ Inf Syst 1:377–436
24.
Geanakoplos J, Pearce D, Stacchetti E (1989) Psychological games and sequential rationality. Games Econ Behav 1:60–79 MathSciNetCrossRef
25.
26.
Gilboa I, Schmeidler D (1988) Information dependent games: can common sense be common knowledge? Econ Lett 27:215–221 MathSciNetCrossRef
27.
Glazer A, Konrad K (1996) A signaling explanation for charity. Am Econ Rev 86:1019–1028
28.
Glicksberg IL (1952) A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proceed Am Math Soc 3:170–174 MathSciNetMATH
29.
Gradwohl R, Smorodinsky R (2014) Subjective perception games and privacy. CoRR, abs/1409.1487
30.
31.
Harrington JE Jr, Zhao W (2012) Signaling and tacit collusion in an infinitely repeated Prisoners’ Dilemma. Math Soc Sci 64(3):277–289
32.
33.
Ireland N (1994) On limiting the market for status signals. J Publ Econ 53:91–110 CrossRef
34.
35.
36.
Madden M, Rainie L, Zickuhr K, Duggan M, Smith A (2014) Public perceptions of privacy and security in the post-snowden era. Pew Res Center 12(9):e0184525
37.
Mailath GJ, Samuelson L (2006) Repeated games and reputations: long-run relationships. Oxford University Press, Oxford
38.
Maor C, Solan E (2015) Cooperation under incomplete information on the discount factors. Int J Game Theory 44:321–346 MathSciNetCrossRef
39.
Maschler M, Solan E, Zamir S (2013) Game Theory. Cambridge University Press, Cambridge CrossRef
40.
McSherry F, Talwar K (2007) Mechanism design via differential privacy. In: Foundations of computer science, 2007. FOCS’07. 48th Annual IEEE Symposium on. IEEE, pp 94–103
41.
Nissim K, Orlandi C, Smorodinsky R (2012a) Privacy-aware mechanism design. In: Proceedings of the 13th ACM Conference on Electronic Commerce. ACM, pp 774–789
42.
Nissim K, Smorodinsky R, Tennenholtz M (2012b) Approximately optimal mechanism design via differential privacy. In: Proceedings of the 3rd innovations in theoretical computer science conference. ACM, pp 203–213
43.
Osborne MJ, Rubinstein A (1994) A course in game theory. MIT press, Cambridge MATH
44.
Posner RA (1981) The economics of privacy. Am Econ Rev 71:405–409
45.
Prat A (2005) The wrong kind of transparency. Am Econ Rev 95:862–877 CrossRef
46.
47.
48.
Royden HL, Fitzpatrick P (1988) Real analysis. Macmillan, New York MATH
49.
Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica J Econ Soc. 97–109
50.
Sobel J (2009) Signaling games. Encyclopedia of complexity and systems science. Springer, Newyork, pp 8125–8139 CrossRef
51.
Taylor CR (2004) Consumer privacy and the market for customer information. RAND J Econ 35:631–650 CrossRef
Metadaten
Titel
Privacy, Patience, and Protection
verfasst von
Ronen Gradwohl
Rann Smorodinsky
Publikationsdatum
21.04.2021
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 4/2021
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00386-z

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