Embedding Trust: A Game-Theoretic Model for Investments in and Returns on Network Embeddedness

Abstract

Social relations through which information disseminates promote efficiency in social and economic interactions that are characterized by problems of trust. This provides incentives for rational actors to invest in their relations. In this article, we study a game-theoretic model in which two trustors interact repeatedly with the same trustee and decide, at the beginning of the game, whether to invest in establishing an information exchange relation between one another. We show that the costs the trustors are willing to bear for establishing the relation vary in a non-monotonic way with the severity of the trust problem. The willingness to invest in the information exchange relation is high particularly for trust problems that are neither too small nor too severe.

Keywords:

• embeddedness
• game theory
• network formation
• reputation
• social dilemmas

Notes

¹Throughout the article, we use standard game theory terminology and assumptions. See, e.g., Fudenberg and Tirole (2000) for a textbook.

²Alternatively, the trustee might have the desire but not the opportunity to abuse trust.

³It could alternatively be assumed that trustor 1 always interacts with the trustee in the odd periods while trustor 2 always plays in the even periods. The analysis of this alternative scenario yields very similar but somewhat more complicated results.

⁴In the game Γ, the set of sequential equilibria coincides with the set of perfect Bayesian equilibria. That is, a combination of beliefs and strategies that is a sequential equilibrium of Γ⁺or Γ⁻ is also a perfect Bayesian equilibrium of the respective continuation game (see Fudenberg & Tirole, 2000, Theorem 8.2).

⁵While the trustee becomes more likely to abuse trust as the end of the game approaches, the trustors randomize with a constant probability.

⁶Note that π and RISK also determine the trustor's expected payoff for the period in which the opportunistic trustee starts to randomize (X₁). The stage-game payoffs of the trustee only determine the randomization probability of the trustors but do not affect their expected payoffs.

⁷The specification of Γ implies that, as and , r₁ is identical for the two trustors.

⁸In other words, the “endgame” of τ TGs in which trust and trustworthiness are not certain anymore occurs for each trustor separately and in its full length in Γ⁻. In Γ⁺, however, the endgame occurs only once and each trustor plays in half of the τ TGs of the endgame.

⁹It can be seen from Figure 2 that the increase towards the maximum and the decrease thereafter is not linear even though r₁ depends linearly on π for changes in π that do not affect τ because the range of π for which τ is constant is smaller, the smaller π.

¹⁰We owe this remark to an anonymous reviewer.

¹¹Given this alternative investment rule, the relation will get established in equilibrium by the investment of one trustor if r₁ > C, although this does create coordination problems similar to a Chicken Game. If C ≥ r₁ ≥ C/2, it will be an equilibrium that the trustors establish the relation jointly and if r₁ < C/2, there cannot be an equilibrium such that the relation gets established.

¹²Note that we count periods forward starting with 1 counting up to 2N, whereas in Buskens (2003), as in many of the related papers, periods are counted backward such that the last period is period 1.