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Bargaining in Markets with One-Sided Competition: Model and Analysis Nicola Gatti

Bargaining in Markets with One-Sided Competition: Model and Analysis Nicola Gatti ngatti@elet.polimi.it DEI, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, 20133, Italy. Results Overview.

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Bargaining in Markets with One-Sided Competition: Model and Analysis Nicola Gatti

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  1. Bargaining in Markets with One-Sided Competition: Model and Analysis Nicola Gatti ngatti@elet.polimi.it DEI, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, 20133, Italy

  2. ResultsOverview The paperaims at studyingmodelsforbilateralnegotiationswithrationalagentswhenthey are in competition • Modelingresult: extensionof the alternating-offersprotocolto the situation wherein: • There are more buyersand one seller, and • The seller can exploit the outside-option • Algorithmicresult: developmentofanefficientsolvingalgorithmforcomputingagents’ equilibriumstrategies (thisresultisnotdiscussed in the presentation)

  3. Bilateral Negotiation (Bargaining) 10$ 11$ Buyer Seller 12$ ...

  4. Alternating-Offers Protocol • Game theoreticalmechanismforbilateralnegotiation[Rubinstein, Econometrica, 1982] • A buyer and a seller wantstonegotiate in analternate-fashion with discrete time • Someonedecides the agentthatstartstomakeoffers • Timediscountsagents’ utilities (so agentsprefertoreach agreement assoonaspossible) • Agents are supposedtoberational, i.e., theyactaiming at maximizingtheirexpected utility • The solutionis a pairofstrategies, a buyer’sone and a seller’sone, that are in equilibrium (typically, refinementof Nash)

  5. The Formal Model [Di Giunta and Gatti, 2006] • Players • Player function • Actions • Preferences 0 1 2 3 4 5 6 7

  6. Bargaining in Markets • More buyersand more sellersare present in a market • More buyers are in competitionover the purchaseofan item from the same seller • More sellers are in competitionover the sale ofan item to the same buyer • The alternating-offersprotocoldoesnotcapturethiscompetition • Weextend the alternating-offersprotocoltocapture: • The matchingbetween a buyer and a seller • The possibilityofleaving a negotiationto start a newonewith a different commercial partner • Weconsider a situation with a seller and more buyers

  7. Bilateral Negotiation with Outside-Option Buyer 1 15$ 11$ Buyer 2 Seller Buyer 3 14$ accept Buyer 4

  8. The Formal Model Devoted to matching Devoted to negotiation 0 1 2 3 4 5 6 7

  9. Closing Remarks • The proposed model allows one to effectively capture competition among agents: • With one seller and more buyers, the seller gainsdrastically more thanagainst the weakest buyer • The computation of agents’ equilibrium strategies is easy (linear in the size of the problem) • In future, we will investigate: • The comparison between the agents’ expected utilities in our protocol with respect to the ones in multilateral negotiations • The analysis of negotiations with uncertainty

  10. Questions Email to: ngatti@elet.polimi.it

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