Bargaining models



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Bargaining models

  • Bargaining models

    • Classical: Nash (Ecta, 1950); Rubinstein (Ecta, 1982); Rubinstein and Wolinsky (Ecta, 1985); Rubinstein and Wolinsky (RES, 1990).
    • Evolutionary: Young (JET, 1993), Binmore et al. (JET, 1998), Young (RES, 1998), Sáez-Martí and Weibull (JET, 1999).
    • On networks: Calvo-Armengol (2001, 2003); Corominas-Bosch (JET, 2004); Polanski (JET, 2008); Manea (2008); Abreu and Manea (2008).
  • Empirical evidence

    • Wholesale markets: Kirman and Vignes (1991); Hardle and Kirman (JE, 1995); Kirman et al. (JEBO, 2005); Vignes et al. (2008).
    • International trade: Rauch (JEL, 2001); Rauch and Trindade (REStud, 2002; AER, 2003); Kumagai (2007).
    • Illegal markets: Levitt and Venkatesh (QJE, 2000; 2007).






























Graddy (RAND, 1995) tracked all (n=489) transactions of whiting by one dealer over 19 days, recording: price, quantity, exact time, type of buyer and quality of fish.

  • Graddy (RAND, 1995) tracked all (n=489) transactions of whiting by one dealer over 19 days, recording: price, quantity, exact time, type of buyer and quality of fish.

  • No posted prices and dealer is free to charge a different price to each customer.

  • “Spread of prices throughout the day is very high, and the interday volatility is large” (Graddy, p. 78).

  • Types of buyers:

    • Three ethnic groups: whites, Asians and blacks (small sample).
    • Locations: Manhattan, Brooklyn, New Brunswick, Princeton.
    • Establishments: restaurants, stores, shippers, dealers, fry shops.


Key finding: white sellers charge white buyers significantly (~7%) more than Asian buyers for the same homogeneous product.

  • Key finding: white sellers charge white buyers significantly (~7%) more than Asian buyers for the same homogeneous product.

  • Graddy (p. 87) concludes that “the reason behind the price discrimination is less clear.”

  • Not a typical setting for 3rd degree price discrimination: competitive industry, no search costs, homogeneous products, no barriers to entry, no significant difference in elasticity for Asians vs white buyers.

  • Graddy (1995) shows that difference is not due to differences in purchase times, product quality, mode of payment and volume of transactions.



A potential explanation: Asian buyers’ communication network is denser/more homogeneous than white buyers’. Therefore, the group of Asian buyers is better at sharing information on today’s price and this informational advantage leads to the observed price difference.

  • A potential explanation: Asian buyers’ communication network is denser/more homogeneous than white buyers’. Therefore, the group of Asian buyers is better at sharing information on today’s price and this informational advantage leads to the observed price difference.

    • Graddy (p. 84): “very little social contact appears to take place between groups of Asian buyers and groups of white buyers”
    • Graddy (p. 87): “Asian buyers appear to be more organized than white buyers”
    • Graddy: “Asian buyers certainly spoke to one another and congregated much more frequently than white buyers”
    • Homophily is a powerful determinant of social networks, and racial/ethnic homophily is much stronger than other types (e.g., McPherson et al., 2001)
    • Evidence that Asian immigrant groups form very close-knit networks (e.g., Sanders et al., 2002; McCabe, 2006)


Asians obtain a better price only after the first 1-2 hours of the market, presumably due to learning.

  • Asians obtain a better price only after the first 1-2 hours of the market, presumably due to learning.

  • Regression analysis shows that the “Asian” dummy is negatively correlated (p=0.01) with prices in the 6-7am time period, but it is statistically insignificant (and positively correlated) in the 4-5am time period.



The variability of prices paid by Asians decreases faster than the variability of prices paid by Whites pointing to faster learning among Asians of the current value of fish.

  • The variability of prices paid by Asians decreases faster than the variability of prices paid by Whites pointing to faster learning among Asians of the current value of fish.



Social connections play a key role in business transactions in the overseas Asian community:

  • Social connections play a key role in business transactions in the overseas Asian community:

  • Redding, Overseas Chinese Networks: Understanding the Enigma, 1995:

    • "[p]ersonalism does in Asia what law does in the West [...] [w]ithout [what is termed guanxi or connections] nothing can be made to happen [...] the instinct of the Overseas Chinese to trust friends but no-one else is very deep-rooted.“
    • “For the Overseas Chinese the uncertainties of the business environment mean that playing fields are not level. […] So the Chinese rules are: put your trust primarily in 'your own' people; seek the opportunities by trading rare information; share that information to build allegiances”
  • Xie, Asian Americans: A Demographic Portrait, 2004:.

    • “Asian American communities offer many practical resources to immigrants, including [...] information in native languages, and entrepreneurial opportunities.“
  • See, e.g., additional references in Rauch and Trindade (REStud, 2002), Rauch and Casella (EJ,2003), Kumagai (2007).



Assume that the two groups share the same network, i.e. buyers receive information from other buyers and sellers about past sellers’ demands, then:

  • Assume that the two groups share the same network, i.e. buyers receive information from other buyers and sellers about past sellers’ demands, then:

    • The stochastically stable division is unchanged.
    • Core-periphery networks maximize the share for a group.
    • A more homogeneous network narrows down the difference between the two groups.
    • In a regular network with homogeneous agents 50-50 is the stable division.


Theoretical

  • Theoretical

    • How sensitive are the results to the assumptions of a very small ε?
    • Can we say anything on the speed to convergence?
  • Empirical

    • How do we test the model empirically?
      • Field experiment?
      • Lab experiment?


Main results:

  • Main results:

  • The unique stochastically stable division is the ANB with weights determined by the players with the least weighted degree in each group.

  • Quasi-regular networks maximize the share for a group.

  • Denser and more homogeneous networks fare better.

  • An empirical analysis of the observed price differential between Asian and white buyers in the FFM is consistent with these predictions

  • If the two groups share the same network, then:

  • The stochastically stable division is unchanged.

  • Core-periphery networks maximize the share for a group.

  • A more homogeneous network narrows down the difference between the two groups.

  • In a regular network with homogeneous agents 50-50 is the stable division.





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