Abstract
This paper studies potential games allowing the possibility that players have incomplete preferences and empty best-response sets. We define four notions of potential games, ordinal, generalized ordinal, best-response, and generalized best-response potential games, and characterize them using cycle conditions. We study Nash equilibria of potential games and show that the set of Nash equilibria remains the same when every player's preferences are replaced with the smallest generalized (best-response) potential relation or a completion of it. Similar results are established about strict Nash equilibria of ordinal and best-response potential games. Lastly, we examine the relations among the four notions of potential games as well as pseudo-potential games.
| Original language | English |
|---|---|
| Pages (from-to) | 58-66 |
| Number of pages | 9 |
| Journal | Journal of Mathematical Economics |
| Volume | 61 |
| DOIs | |
| Publication status | Published - 2015 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Economics and Econometrics
- Applied Mathematics
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Potential games with incomplete preferences. / Park, Jaeok.
In: Journal of Mathematical Economics, Vol. 61, 01.01.2015, p. 58-66.Research output: Contribution to journal › Article
TY - JOUR
T1 - Potential games with incomplete preferences
AU - Park, Jaeok
PY - 2015/1/1
Y1 - 2015/1/1
N2 - This paper studies potential games allowing the possibility that players have incomplete preferences and empty best-response sets. We define four notions of potential games, ordinal, generalized ordinal, best-response, and generalized best-response potential games, and characterize them using cycle conditions. We study Nash equilibria of potential games and show that the set of Nash equilibria remains the same when every player's preferences are replaced with the smallest generalized (best-response) potential relation or a completion of it. Similar results are established about strict Nash equilibria of ordinal and best-response potential games. Lastly, we examine the relations among the four notions of potential games as well as pseudo-potential games.
AB - This paper studies potential games allowing the possibility that players have incomplete preferences and empty best-response sets. We define four notions of potential games, ordinal, generalized ordinal, best-response, and generalized best-response potential games, and characterize them using cycle conditions. We study Nash equilibria of potential games and show that the set of Nash equilibria remains the same when every player's preferences are replaced with the smallest generalized (best-response) potential relation or a completion of it. Similar results are established about strict Nash equilibria of ordinal and best-response potential games. Lastly, we examine the relations among the four notions of potential games as well as pseudo-potential games.
UR - http://www.scopus.com/inward/record.url?scp=84948771007&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84948771007&partnerID=8YFLogxK
U2 - 10.1016/j.jmateco.2015.07.007
DO - 10.1016/j.jmateco.2015.07.007
M3 - Article
AN - SCOPUS:84948771007
VL - 61
SP - 58
EP - 66
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
SN - 0304-4068
ER -