Skip to main content
SpringerLink
Log in

Resolving the Trust Predicament: A Quantum Game-theoretic Approach

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

Developing a good theoretical understanding of the role of trust in IR (such as in the events leading to the end of the Cold War) is still an open problem. Most game-theoretic studies of trust do not go beyond the limitations of an (ontologically) individualistic paradigm, thus assuming a pre-defined set of individual strategies. Yet, it is a fact that the predicament of collective trust is empirically resolved in many situations. This paper suggests a new game-theoretic approach—Quantum Game Theory (QGT)—to understand and explain how the predicament of trust is resolved. In a quantum game of trust the actors play the game by simultaneously collectively reconstructing the strategic environment in such a way as to become mutually strategically entangled. Quantum strategic entanglement allows trust to emerge between the two actors without assuming a need for signaling, prior “contract” type of arrangement, or any form of third-party communication. The paper develops and solves such a model of quantum game of trust

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abouraddy A.F. et al. (2001). Degree of entanglement for two qubits. Physical Review A 64, 050101(R), 1–4.

    Google Scholar 

  • E. Adler M. Barnett (Eds) (1998) Security Communities Cambridge University Press New York

    Google Scholar 

  • D. Aerts J. Broekaert S. Smets (1999) ArticleTitleThe Liar-paradox in a quantum mechanical perspective Foundations of Science 4 115–132

    Google Scholar 

  • A. Boukas (2000) ArticleTitleQuantum formulation of classical two-person zero-sum games Open Systems and Information Dynamics 7 19–32 Occurrence Handle10.1023/A:1009699300776

    Article  Google Scholar 

  • G. Brennan (1998) Democratic trust: a rational-choice theory view Braithwaite Valerie Levi Margaret (Eds) Trust and Governance Russell Sage Foundation New York 197–217

    Google Scholar 

  • B. Chapman (1998) ArticleTitleMore easily done than said: rules, reason and rational social choice Oxford Journal of Legal Studies 18 293–329 Occurrence Handle10.1093/ojls/18.2.293

    Article  Google Scholar 

  • L.K. Chen H. Ang D. Kianga L.C. Kwek C.F. Lo (2003) ArticleTitleQuantum prisoner dilemma under decoherence Physics Letters A 316 317–323

    Google Scholar 

  • K-Y. Chen T. Hogg R. Beausoleil (2002a) ArticleTitleA quantum treatment of public goods economics Quantum Information Processing 1 IssueID6 449–469 Occurrence Handle10.1023/A:1024070415465

    Article  Google Scholar 

  • Jing-Ling Chen L.C. Kwek C. H. Oh (2002b) ArticleTitleNoisy quantum game Physical Review A 65 0523201–0523206

    Google Scholar 

  • J. Derrida (1978) Writing and Difference Routledge & Kegan Paul London

    Google Scholar 

  • M. Dresher (1981) The Mathematics of Games of Strategy Dover New York

    Google Scholar 

  • J. Du H. Li X. Xu X. Zhou R. Han (2002) ArticleTitleEntanglement enhanced multiplayer quantum games Physics Letters A 302 IssueID5 229–233 Occurrence Handle10.1016/S0375-9601(02)01144-1

    Article  Google Scholar 

  • J. Du H. Li X. Xu X. Zhou R. Han (2003) ArticleTitlePhase-transition-like behaviour of quantum games Journal of Physics A: Mathematical and General 36 IssueID23 6551–6562 Occurrence Handle10.1088/0305-4470/36/23/318

    Article  Google Scholar 

  • Jiangfeng Du H. Li C. Ju (2003b) ArticleTitleQuantum games of asymmetric information Physical Review E 68 0161241–0161245 Occurrence Handle10.1103/PhysRevE.68.016124

    Article  Google Scholar 

  • J. Eisert M. Lewenstein (1999) ArticleTitleQuantum games and quantum strategies Physical Review Letters 83 3077–3080 Occurrence Handle10.1103/PhysRevLett.83.3077

    Article  Google Scholar 

  • J. Eisert M. Wilkens (2000) ArticleTitleQuantum games Journal of Modern Optics 47 IssueID14 2543–2556 Occurrence Handle10.1080/095003400750039537

    Article  Google Scholar 

  • J. Eisert M. Wilkens M. Lewenstein (1999) ArticleTitleQuantum games and quantum strategies Physical Review Letters 83 IssueID15 3077–3080 Occurrence Handle10.1103/PhysRevLett.83.3077

    Article  Google Scholar 

  • A.P. Flitney D. Abbott (2002a) ArticleTitleQuantum version of the Monty Hall problem Physical Review A 65 062318 Occurrence Handle10.1103/PhysRevA.65.062318

    Article  Google Scholar 

  • A.P. Flitney D. Abbot (2002) ArticleTitleAn introduction to quantum game theory Fluctuation and Noise Letters 2 IssueID4 R175–R187

    Google Scholar 

  • A.P. Flitney J. Ng D. Abbott (2002) ArticleTitleQuantum Parrondo’s games Physica A 314 IssueID1 35–42 Occurrence Handle10.1016/S0378-4371(02)01084-1

    Article  Google Scholar 

  • A.P. Flitney D. Abbott (2003) ArticleTitleAdvantage of a quantum player over a classical one in 2 × 2 quantum games Proceedings: Mathematical, Physical and Engineering Sciences 459 IssueID2038 2463–2474 Occurrence Handle10.1098/rspa.2003.1136

    Article  Google Scholar 

  • R. L. Garthoff (1994) The Great Transition The Brookings Institute Washington DC

    Google Scholar 

  • Grib A. and Parfionov, G. (2003), Can the game be quantum? arXiv: quant-ph/0206178.

  • F. Guinea M.A. Martin-Delgado (2003) ArticleTitleQuantum Chinos game: winning strategies through quantum fluctuations Journal of Physics A: Mathematical and General 36 IssueID13 197–204 Occurrence Handle10.1088/0305-4470/36/13/104

    Article  Google Scholar 

  • Y. Han Y.-S. Zhang G. Guo (2002) ArticleTitleW State and Greenberger-Horne-Zeilinger state in quantum three-person prisoner’s dilemma Physics Letters A 295 IssueID2 61–64 Occurrence Handle10.1016/S0375-9601(02)00168-8

    Article  Google Scholar 

  • J. Harsanyi (1977) Rational Behavior and Bargaining Equilibrium in Games and Social Situations Cambridge University Press New York

    Google Scholar 

  • J. Harsanyi R. Selten (1988) A General Theory of Equilibrium Selection in Games MIT Press Cambridge, MA

    Google Scholar 

  • S. Hill W. Wootters (1997) ArticleTitleEntanglement of a pair of quantum bits Physical Review Letters 78 IssueID26 5022–5025 Occurrence Handle10.1103/PhysRevLett.78.5022

    Article  Google Scholar 

  • A. Iqbal A.H. Toor (2001) ArticleTitleEvolutionary stable strategies in quantum games Physics Letters A 280 249 Occurrence Handle10.1016/S0375-9601(01)00082-2

    Article  Google Scholar 

  • A. Iqbal A.H. Toor (2002a) ArticleTitleDarwinism in quantum systems? Physics Letters A 294 IssueID5 261–270 Occurrence Handle10.1016/S0375-9601(02)00067-1

    Article  Google Scholar 

  • A. Iqbal A.H. Toor (2002b) ArticleTitleQuantum cooperative games Physics Letters A 293 IssueID3 103–108 Occurrence Handle10.1016/S0375-9601(02)00003-8

    Article  Google Scholar 

  • A. Iqbal A.H. Toor (2002) ArticleTitleQuantum repeated games Physics Letters A 300 IssueID6 541–546 Occurrence Handle10.1016/S0375-9601(02)00893-9

    Article  Google Scholar 

  • R. Jervis (1988) ArticleTitleRealism, game theory, and cooperation World Politics 40 IssueID3 317–349

    Google Scholar 

  • R. Kay N.F. Johnson S.C. Benjamin (2001) ArticleTitleEvolutionary quantum game Journal of Physics A: Mathematical and General 34 IssueID41 547–552 Occurrence Handle10.1088/0305-4470/34/41/101

    Article  Google Scholar 

  • Robert O. Keohane L.L. Martin (1995) ArticleTitleThe promise of institutionalist theory International Security 20 IssueID1 39–51

    Google Scholar 

  • J. Kim (1984) ArticleTitleConcepts of supervenience Philosophy and Phenomenological Research 45 153–76

    Google Scholar 

  • A. Kydd (2000) ArticleTitleTrust, reassurance, and cooperation International Organization 54 IssueID2 325–57 Occurrence Handle10.1162/002081800551190

    Article  Google Scholar 

  • D. Lake R. Powell (Eds) (1999) Strategic Choice and International Relations Princeton University Press Princeton, NJ

    Google Scholar 

  • Deborah W. Larson (1997) ArticleTitleTrust and missed opportunities in international relations Political Psychology 18 IssueID3 701–734 Occurrence Handle10.1111/0162-895X.00075

    Article  Google Scholar 

  • D. Lax J.K. Sebenius (1986) The Manager as Negotiator Free Press New York

    Google Scholar 

  • C.F. Lee N.F. Johnson (2003) ArticleTitleQuantum game theory Physical Review A 67 022311

    Google Scholar 

  • H. Li J. Du S. Massar (2002) ArticleTitleContinuous-variable quantum games Physics Letters A 306 IssueID2 73–78 Occurrence Handle10.1016/S0375-9601(02)01628-6

    Article  Google Scholar 

  • Y.J. Ma G.L. Long F.G. Deng F. Li S.X. Zhang (2002) ArticleTitleCooperative three- and four-player quantum games Physics Letters A 301 IssueID3 117–124 Occurrence Handle10.1016/S0375-9601(02)00989-1

    Article  Google Scholar 

  • Marinatto L., Weber T. (2000), A quantum approach to static games of complete information. Physics Letters A 272, 291.

    Google Scholar 

  • F. McGillivray A. Smith (2000) ArticleTitleTrust and cooperation through agent-specific punishments International Organization 54 IssueID4 809–824 Occurrence Handle10.1162/002081800551370

    Article  Google Scholar 

  • J.J. Mearsheimer (1991) Back to the future: instability in Europe after the cold war Sean M. Lynn-Jones (Eds) The Cold War and After MIT Press Cambridge, MA 141–192

    Google Scholar 

  • D. Meyer (1999) ArticleTitleQuantum strategies Physical Review Letters 82 1052 Occurrence Handle10.1103/PhysRevLett.82.1052

    Article  Google Scholar 

  • A. Nawaz A.H. Toor (2004) ArticleTitleDilemma and quantum battle of sexes Journal of Physics A: Mathematical and General 37 IssueID15 4437–4443 Occurrence Handle10.1088/0305-4470/37/15/011

    Article  Google Scholar 

  • H.T. Nguyen V. Kreinovich V. Shekhter (1998) ArticleTitleOn the possibility of using complex values in fuzzy logic for representing inconsistencies International Journal of Intelligent Systems 13 683–714 Occurrence Handle10.1002/(SICI)1098-111X(199808)13:8<683::AID-INT1>3.0.CO;2-F

    Article  Google Scholar 

  • E.W. Piotrowski J. Sladkowski (2002a) ArticleTitleQuantum bargaining games Physica A 308 IssueID1 391–401

    Google Scholar 

  • E.W. Piotrowski J. Sladkowski (2002b) ArticleTitleQuantum market games Physica A 312 IssueID1 208–216 Occurrence Handle10.1016/S0378-4371(02)00842-7

    Article  Google Scholar 

  • E.W. Piotrowski J. Sladkowski (2003a) ArticleTitleQuantum English auctions Physica A 318 IssueID3 505–515

    Google Scholar 

  • E.W. Piotrowski J. Sladkowski (2003b) ArticleTitleTrading by quantum rules: quantum anthropic principle International Journal of Theoretical Physics 42 IssueID5 1101–1106

    Google Scholar 

  • E.W. Piotrowski J. Sladkowski (2001) ArticleTitleQuantum-like approach to financial risk: quantum anthropic principle Acta Physica Polonica B 32 3873

    Google Scholar 

  • E.W. Piotrowski J. Sladkowski J. Syska (2003) ArticleTitleInterference of quantum market strategies Physica A 318 IssueID3 516–528

    Google Scholar 

  • E.W. Piotrowski J. Sadkowski (2003c) ArticleTitleAn invitation to quantum game theory International Journal of Theoretical Physics 42 IssueID5 1089–1099

    Google Scholar 

  • Piotrowski E. W. (2003), The next stage: quantum game theory. arXiv: quant-ph/0308027.

  • I. Pitowsky (1986) ArticleTitleThe range of quantum probability Journal of Mathematical Physics 27 IssueID6 1556–1565 Occurrence Handle10.1063/1.527066

    Article  Google Scholar 

  • A. Plotnisky (1994) Complementarity: Anti-Epistemology after Bohr and Derrida Duke University Press Durham, CT

    Google Scholar 

  • J.R. Searle (1995) The Construction of Social Reality The Free Press New York

    Google Scholar 

  • J. Sladkowski (2003) ArticleTitleGiffen paradoxes in quantum market games Physica A 324 IssueID1 234–240 Occurrence Handle10.1016/S0378-4371(02)01859-9

    Article  Google Scholar 

  • A. Stein (1999) The limits of strategic choice: constrained rationality and incomplete explanation David Lake Robert Powell (Eds) Strategic Choice and International Relations Princeton University Press Princeton, NJ 196–228

    Google Scholar 

  • S. Waite (2002) Quantum Investing Texere Publishing London

    Google Scholar 

  • J. Watson (1999) ArticleTitleStarting small and renegotiation Journal of Economic Theory 85 52–90 Occurrence Handle10.1006/jeth.1998.9999

    Article  Google Scholar 

  • B.R. Weingast (1998) Constructing trust: the political and economic roots of ethnic and regional conflict Karol Sultan Eric M. Uslaner Virginia Haufler (Eds) Institutions and Social Order The University of Michigan Press Ann Arbor, MI 163–200

    Google Scholar 

  • W. Wootters (1998) ArticleTitleEntanglement of formation of an arbitrary state of two qubits Physical Review Letters 80 IssueID10 2245–2248 Occurrence Handle10.1103/PhysRevLett.80.2245

    Article  Google Scholar 

  • P. Zelikow C. Rice (1995) Germany Unified and Europe Transformed Harvard University Press Cambridge MA

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Political Science, University of Florida, 234 Anderson Hall, Box 117325, Gainesville, FL, 32611-7325, U.S.A

    Badredine Arfi

Authors
  1. Badredine Arfi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Badredine Arfi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arfi, B. Resolving the Trust Predicament: A Quantum Game-theoretic Approach. Theor Decis 59, 127–174 (2005). https://doi.org/10.1007/s11238-005-8632-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-005-8632-4

Keywords

Search

Navigation