International Governance and Risk Management by Toshihiro Ihori & Martin C. McGuire & Shintaro Nakagawa

Author:Toshihiro Ihori & Martin C. McGuire & Shintaro Nakagawa
Language: eng
Format: epub
ISBN: 9789811388750
Publisher: Springer Singapore

5.2.3 Interior Nash Equilibria

5.2.3.1 Treatment of Cost-Input as Public Good

Now, to exploit the advantages of “summation financing” instead of the conventional expression for expected welfare, i.e. , we propose—as described elsewhere in the literature (e.g. Cornes and Hartley 2005)—to work with “induced” preferences over and M and adjust terminology slightly so that M is called a “public good”. An increase in M at given changes the welfare of both parties (in the relevant range raises welfare) even though M is not itself directly an object of consumption per se; nor is it an argument in the conventional direct expected utility function . But providing this “public good” does instrumentally raise expected utility of consuming the private good for both parties in a non-rival non-excluded fashion. Moreover, so long as the Nash equilibrium is interior so that both parties make positive contributions, M is effectively chosen by and agreed on by both as noted first by Becker (1974).

We want to introduce this innovation, extending the term “public good” to the indirect productive input, M, because doing so permits us to use conventional geometric properties of the VPG model to derive and illustrate the unconventional insights of this article. These relate to connections among (a) risk aversion in the utility function, (b) status quo risk, (c) normality/inferiority of the public good M, (d) stability and therefore attainability of Nash solutions, and (e) effects of group size on equilibrium. Thus, in place of Eq. (5.1′)—i.e. —we will write a country’s expected welfare objective function as:

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