Non-additive anonymous games

International Journal of Game Theory

Volumn 40, Issue 2, 2011, Pages 215-230

  Kozhan, Roman ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Anonymous game; Capacity; Non additive measure; Uncertainty

Indexed keywords

EID: 79957499608     PISSN: 00207276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00182-010-0235-9     Document Type: Article

References (46)

1. Aliprantis Ch, Glycopantis D, Puzzello D (2006) The joint continuity of the expected payoffs functions. J Math Econ 42: 121-130.
2. Camerer C, Ho T (1994) Violations of the betweenness of axiom and nonlinearity in probability. J Risk Uncertainty 8: 167-196.
3. Choquet G (1953) Theory of capacities. Annales de l'Institut Fourier 5: 131-295.
4. Curley S, Yates F (1989) An empirical evaluation of descriptive models of ambuguity reactions in choice situations. J Math Psychol 33: 397-427.
5. Denneberg D (1994) Non-additive measure and integral. Kluwer Academic Publishers, Dordrecht.
6. Dow J, Werlang S (1994) Nash equilibrium under Knightian Uncertainty: breaking down backward induction. J Econ Theory 64(2): 305-324.
7. Eichberger J, Kelsey D (1999) Education signalling and uncertainty. unpublished, University of Birmingham.
8. Eichberger J, Kelsey D (2000) Non-additive beliefs and strategic equilibria. Games Econ Behav 30: 183-215.
9. Eichberger J, Kelsey D (2004) Sequential two-player games with ambiguity. Int Eco Rev 45(4): 1229-1261.
10. Eilenberg S, Moore J (1965) Adjoint functors and triples. Ill J Math 9: 381-398.
11. Ellsberg D (1961) Risk, ambiguity and the Savage axioms. Q J Econ 75: 643-669.
12. Fan K (1952) Fixed-point minimax theorems in locally convex topological linear spaces. Proc Natl Acad Sci USA 38: 121-126.
13. Ghirardato P, LeBreton M (2000) Choquet rationality. J Econ Theory 90: 277-285.
14. Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J Math Econ 18: 141-153.
15. Glycopantis D, Muir A (1999) Nash equilibria in ∞-dimensional spaces: an approximation theorem. Econ Theory 13: 743-751.
16. Glycopantis D, Muir A (2000) Continuiuty of the payoff function. Econ Theory 16: 239-244.
17. Glycopantis D, Muir A (2008) Nash equilibria with Knightian uncertainty; the case of capacities. Econ Theory 37(1): 147-159.
18. Green E (1984) Continuum and finite-player noncooperative models of competition. Econometrica 52(4): 975-994.
19. Groes E, Jacobsen H, Sloth B, Tranaes T (1998) Nash equilibrium in lower probabilities. Theory Decis 44: 37-66.
20. Hart S, Hildenbrand W, Kohlberg E (1974) On equilibrium allocations as distributions on the commodity space. J Math Econ 1: 159-166.
21. Hogarth R, Einhorn H (1990) Venture theory: a model of desicion weights. Manag Sci 36: 780-803.
22. Kajii A, Morris S (1998) Payoff continuity in incomplete information games. J Econ Theory 82: 267-276.
23. Khan A, Sun Y (1987) On symmetric Cournot-Nash equilibrium distributions in a finite-action, atomless game. In: Khan A, Yennelis N Equilibrium theory in infinite dimensional spaces. Sprimger, Berlin.
24. Khan A, Sun Y (1995) Extremal structures and symmetric equilibria with countable actions. J Math Econ 24: 239-248.
25. Klibanoff P (1996) Uncertainty, decisions, and normal games. Mimeo, MIT.
26. Knight F (1921) Risk, uncertainty and profit. Houghton Miffin, Boston.
27. Kozhan R (2006) Open-multicommutativity of the functor of capacities, Visnyk of Lviv University, Working Paper Nr.: math. GN/0610678. Series Mechanical and Mathematical, vol 70. www. arxiv. org.
28. Kozhan R, Zarichnyi M (2008) Nash equilibria for games in capacities. Econ Theory 35: 321-331.
29. Lo K (1996) Equilibrium in beliefs under uncertainty. J Econ Theory 71: 443-484.
30. Marinacci M (1999) Limit laws for non-additive probabilities and their frequentist interpretation. J Econ Theory 84: 145-195.
31. Marinacci M (2000) Ambiguous games. Games Econ Behav 31: 191-219.
32. Mas-Colell A (1986) On a theorem of Schmeidler. J Math Econ 13: 201-206.
33. Michael E (1951) Topologies on spaces of subsets. Trans Am Math Soc 71: 152-182.
34. Milgrom P, Weber R (1985) Distributional strategies for games with incomplete information. Math Oper Res 10(4): 619-632.
35. Mukerji S (1997) Understanding the nonadditive probability decision model. Econ Theory 9: 23-46.
36. Mukerji S, Shin HS (2002) Equilibrium departures from common knowledge in games with non-additive expected utility. Adv Theor Econ 2(1): 2.
37. Nykyforchyn O, Zarichnyi M (2006) The functor of capacities in the catogery of compact hausdorff spaces. Preprint.
38. Rath K, Sun Y, Yamashige S (1995) The nonexistence of symmetric equilibria in anonymous games with compact action spaces. J Math Econ 24: 331-346.
39. Ryan M (2002) Violations of Belief Persistence in Dempster-Shafer Equilibrium. J Econ Theory 39: 167-174.
40. Savage L (1954) The foundation of statistics. Wiley, New York.
41. Schmeidler D (1973) Equilibrium points of nonatomic games. J Stat Phys 17(4): 295-300.
42. Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571-587.
43. Teleiko A, Zarichnyi M (1999) Categorical topology of compact Hausdorf spaces, vol 5 of Mathematical Studii, Monograph Series. VNTL Publishers, Lviv.
44. Tversky A, Fox C (1995) Weighting risk and uncertainty. Psychol Rev 102: 269-283.
45. Zarichnyi M (1990) On covariant topological functors, I. Quest Answ Gen Topol 8: 317-369.
46. Zhou L (1998) Integral representation of continuous comonotonically additive functionals. Trans Am Math Soc 350(5): 1811-1822.