Preference-Based Unawareness

Schipper, Burkhard C (2011): Preference-Based Unawareness.

Abstract

Morris (1996, 1997) introduced preference-based definitions of knowledge of belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is behaviorally characterized as the event being null and its negation being null.

• Item Type: MPRA Paper
• Language: English
• Keywords: unawareness, awareness, knowledge, preferences, subjective expected utility theory, decision theory, null event
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Agotnes, T. and N. Alechina (2007). Full and relative awareness: A decidable logic for reasoning about knowledge of unawareness, in: Theoretical Aspects of Rationality and Knowledge, Proceedings of the 11th Conference (TARK 2007), Dov Samet (Ed.), Presses Universitaires De Louvain, 6-14.

Board, O. and K.S. Chung (2009). Object-based unawareness: Theory and applications, mimeo., University of Minnesota.

Board, O., Chung, K.S., and B.C. Schipper (2011). Two Models of Unawareness: Comparing the Object-Based and Subjective-State-Space Approaches, Synthese (Knowledge, Rationality and Action), forthcoming.

Dekel, E., Lipman, B. and A. Rustichini (1998). Standard state-space models preclude unawareness, Econometrica 66, 159-173.

van Ditmarsch, H. and T. French (2009). Awareness and forgetting of facts and agents, in: P. Boldi, G. Vizzari, G. Pasi and R. Baeza-Yates, Proceedings of WI-IAT Workshops (WLIAMAS) 2009}, IEEE Press, 478-483.

van Ditmarsch, H. and T. French (2010). Becoming Aware, Proceedings of 3rd Workshop on Logical Aspects of Multi-Agent Systems (LAMAS), Toronto.

Fagin, R. and J.Y. Halpern (1988). Belief, awareness and limited reasoning, Artificial Intelligence 34, 39-76.

Feinberg, Y. (2009). Games with unawareness, mimeo., Stanford University.

Galanis, S. (2010). Syntactic foundations of unawareness of theorems, Theory and Decision, forthcoming.

Galanis, S. (2007). Unawareness of theorems, mimeo., The University of Southampton.

Grant, S. and J. Quiggin (2010). Inductive reasoning about unawareness, mimeo., Rice University.

Halpern, J.Y. (2001). Alternative semantics for unawareness, Games and Economic Behavior 37, 321-339.

Halpern, J. and L.C. Rego (2006). Extensive games with possibly unaware players, in: Proc. Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, 744-751.

Halpern, J. and L. Rego (2008). Interactive unawareness revisited, Games and Economic Behavior 62, 232-262.

Halpern, J. and L. Rego (2009a). Reasoning about knowledge of unawareness, Games and Economic Behavior, forthcoming.

Halpern, J. and L. Rego (2009a). Reasoning about knowledge of unawareness revisited, Proceedings of Twelfth Conference on Theoretical Aspects of Rationality and Knowledge, 166-173.

Heifetz, A., Meier, M. and B. C. Schipper (2006). Interactive unawareness, Journal of Economic Theory 130, 78-94.

Heifetz, A., Meier, M. and B. C. Schipper (2008). A canonical model for interactive unawareness, Games and Economic Behavior 62, 304-324.

Heifetz, A., Meier, M. and B. C. Schipper (2010). Unawareness, beliefs and speculative trade, mimeo., The University of California, Davis.

Heifetz, A., Meier, M. and B.C. Schipper (2011a). Dynamic unawareness and rationalizable behavior, mimeo., The University of California, Davis.

Heifetz, A., Meier, M. and B.C. Schipper (2011b). Prudent rationalizability in generalized extensive-form games, mimeo., The University of California, Davis.

Heifetz, A., Meier, M. and B.C. Schipper (2011c). Conditional dominance in dynamic games with unawareness, mimeo., The University of California, Davis.

Hill, B. (2010). Awareness dynamics, Journal of Philosophical Logic 39, 113-137.

Li J. (2006). Dynamic games of complete information with unawareness, mimeo.

Li J. (2008). A note on unawareness and zero probability, mimeo.

Li, J. (2009). Information structures with unawareness, Journal of Economic Theory 144, 977-993.

Modica, S. and A. Rustichini (1999). Unawareness and partitional information structures, Games and Economic Behavior 27, 265-298.

Morris, S. (1997). Alternative definitions of knowledge, in: Bacharach, M.O.L. et al. (eds.), Epistemic logic and the theory of games and decisions, Kluwer Academic Publishers, 217-233.

Morris, S. (1996). The logic of belief and belief change: A decision theoretic approach, Journal of Economic Theory 69, 1-23.

Meier, M. and B. C. Schipper (2010). Speculative trade under unawareness -- The infinite case, mimeo., The University of California, Davis.

Rego, L. C. and J. Halpern (2007). Generalized solution concepts in games with possibly unaware players, in: Theoretical Aspects of Rationality and Knowledge, Proceedings of the 11th Conference (TARK 2007), Dov Samet (Ed.), Presses Universitaires De Louvain, 253-262.

Rubinstein, A. (1991), Comments on the interpretation of game theory, Econometrica 59, 909-924.

Savage, L.J. (1954). The foundations of statistics, New York: Dover.

Schipper, B.C. (2010). Awareness-dependent subjective expected utility theory, mimeo., University of California, Davis.

Sillari, G. (2008). Quantified logic of awareness and impossible possible worlds, Review of Symbolic Logic 1, 514-529.