Strategic Analysis of Incomplete Preferences on Contingent Markets with a Data Mining Approach

Subject Areas : Multimedia Processing, Communications Systems, Intelligent Systems

Hamid Askari Harooni ¹ , Majid Eshaghi Gorji ²

1 - PhD Student, Department of Mathematics, Semnan University, Semnan, Iran.
2 - Professor, Department of Mathematics, Semnan University, Semnan, Iran

Received: 2024-10-08 Accepted : 2024-11-18 Published : 2025-01-27

Keywords: incomplete preferences, Matching theory, Contingent market, allocation, Decision tree, Data Mining,

Abstract :

Abstract

Introduction: This article explores the occurrence of suspicious betting or trades among individuals with incomplete preferences when they have access to convex choice sets. Unlike standard economic models that often inhibit such trades due to incomplete preferences, our study reveals a significant shift in this paradigm. We argue that decision-makers with shared tastes and attainable sets can mutually benefit from suspicious trades, particularly concerning the allocations of public state. Moreover, we propose a framework that internalizes these allocations, which are traditionally viewed externally in existing literature.

Method: The analysis is structured around a two-stage equilibrium process. In the first stage, isolated individuals assess their attainable sets, denoted as , to determine their individual outcomes or autarky. These individual outcomes become exogenous data for a subsequent exchange equilibrium problem, enabling trade between individuals. This model assumes that individuals can independently and unpredictably acquire their outcomes, engaging in trade without the influence of new markets.

Results: Our findings highlight that when individuals are capable of identifying suspicious trades, particularly in public state allocations, they can enhance their decision-making efficiency. The model reveals that individuals with similar preferences benefit from these trades, leading to effective resource allocation even in the presence of incomplete preferences. Additionally, we present a transferable differential representation of public state allocations, establishing conditions under which suspicious trades emerge or fail to materialize.

Discussion: This exploration significantly contributes to the understanding of economic dynamics involving incomplete preferences and convex choice sets. By providing a framework for internalizing public state allocations, we contrast with the traditional understanding in which these states are viewed as exogenous. Our study highlights the potential for decentralized decision-making among individuals and offers a nuanced perspective on how suspicious trades can facilitate beneficial arrangements in economic interactions. This model encourages a reevaluation of existing theories concerning preference completeness and trade, indicating that avenues for collaboration can exist even within seemingly mismatched preferences.

 

References:

[1] Aumann, R.J., “Utility Theory without the Completeness Axiom,” Econometrica, vol. 30, no. 3, pp. 445-462, 1962.
[2] Bewley, T.F., Knightian Decision Theory: Part 1. 1986, Cowles Foundation Discussion Paper no. 807, Yale University.
[3] Bewley, T.F., “Knightian decision theory. Part I,” Decisions in Economics and Finance, vol. 25, no. 2, pp. 79-110, 2002.
[4] Billot, A., et al., “Sharing beliefs : Between agreeing and disagreeing,” Econometrica, vol. 68, no. 3, pp. 685-694, 2000.
[5] Blackorby, C. and D. Donaldson, “A Theoretical Treatment of Indices of Absolute Inequality,” International Economic Review, vol. 21, no. 1, pp. 107-136, 1980.
[6] Cao, H.H., et al., “Fear of the Unknown: Familiarity and Economic Decisions*,” Review of Finance, vol. 15, no. 1, pp. 173-206, 2011.
[7] Cao, H.H., T. Wang, and H.H. Zhang, “Model Uncertainty, Limited Market Participation, and Asset Prices,” The Review of Financial Studies, vol. 18, no. 4, pp. 1219-1251, 2005.
[8] Chambers, R.G., “Uncertain equilibria and incomplete preferences,” Journal of Mathematical Economics, vol. 55, no., pp. 48-54, 2014.
[9] De Finetti, B., Probability, Induction and Statistics: The Art of Guessing. New York: J. Wiley, 1972.
[10] Dow, J. and W. Sérgio Ribeiro da Costa, “Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio,” Econometrica, vol. 60, no. 1, pp. 197-204, 1992.
[11] Easley, D. and M. O’Hara, “Ambiguity and Nonparticipation: The Role of Regulation,” The Review of Financial Studies, vol. 22, no. 5, pp. 1817-1843, 2009.
[12] Easley, D. and M. O’Hara, “Liquidity and valuation in an uncertain world,” Journal of Financial Economics, vol. 97, no. 1, pp. 1-11, 2010.
[13] Ellsberg, D., “Risk, Ambiguity, and the Savage Axioms,” The Quarterly Journal of Economics, vol. 75, no. 4, pp. 643-669, 1961.
[14] Galaabaatar, T. and E. Karni, “Subjective Expected Utility With Incomplete Preferences,” Econometrica, vol. 81, no. 1, pp. 255-284, 2013.
[15] Hiriart-Urruty, J.B. and C. Lemaréchal, Fundamentals of Convex Analysis. Berlin: Springer Berlin Heidelberg, 2004.
[16] Kajii, A. and T. Ui, “Agreeable bets with multiple priors,” Journal of Economic Theory, vol. 128, no. 1, pp. 299-305, 2006.
[17] Knight, F.H., Risk, Uncertainty and Profit. New York: Cosimo Classics, 2005.
[18] Lashgari, Z., A. Bahiraie, and M. Eshaghi Gordji, “A New Credit and Loan Lending Strategy and Credit in Banking Systems: An Evolutionary Game Theory Approach,” Journal of Applied Mathematics, vol. 2022, no. 1, pp. 1-12, 2022.
[19] Lashgari, Z., et al., “Evolutionary game to model risk appetite of individual investors,” Advances in Systems Science and Applications, vol. 22, no. 1, pp. 35-50, 2022.
[20] Luenberger, D.G., “Dual Pareto Efficiency,” Journal of Economic Theory, vol. 62, no. 1, pp. 70-85, 1994.
[21] Luenberger, D.G., “Optimality and the Theory of Value,” Journal of Economic Theory, vol. 63, no. 2, pp. 147-169, 1994.
[22] Mandler, M., “Incomplete preferences and rational intransitivity of choice,” Games and Economic Behavior, vol. 50, no. 2, pp. 255-277, 2005.
[23] Manteqipour, M. and p. Rahimkhani, “Designing a hybrid model for classification of imbalanced data in the field of third party insurance,” Intelligent Multimedia Processing and Communication Systems (IMPCS), vol. 2, no. 3, pp. 1-9, 1401.
[24] Masatlioglu, Y. and E.A. Ok, “Rational choice with status quo bias,” Journal of Economic Theory, vol. 121, no. 1, pp. 1-29, 2005.
[25] Najafi, M., M. Afzali, and M. Moradi, “Use data mining to identify factors affecting students' academic failure,” Intelligent Multimedia Processing and Communication Systems (IMPCS), vol. 1, no. 2, pp. 23-33, 2021.
[26] Rigotti, L. and C. Shannon, “Uncertainty and Risk in Financial Markets,” Econometrica, vol. 73, no. 1, pp. 203-243, 2005.
[27] Rigotti, L. and C. Shannon, “Sharing risk and ambiguity,” Journal of Economic Theory, vol. 147, no. 5, pp. 2028-2039, 2012.
[28] Rigotti, L., C. Shannon, and T. Strzalecki, “Subjective Beliefs and ex ante Trade,” Econometrica, vol. 76, no. 5, pp. 1167-1190, 2008.
[29] Rockafellar, R.T., Convex Analysis. Princeton: Princeton University Press, 1970.
[30] Savage, L.J., The Foundations of Statistics. New York: Wiley, 1954.
[31] Trojani, F. and P. Vanini, “Robustness and Ambiguity Aversion in General Equilibrium,” Review of Finance, vol. 8, no. 2, pp. 279-324, 2004.
[32] Ui, T., “The Ambiguity Premium vs. the Risk Premium under Limited Market Participation,” Review of Finance, vol. 15, no. 2, pp. 245-275, 2011.
[33] Walley, P., Statistical Reasoning with Imprecise Probabilities. London: Chapman & Hall, 1990.