Games

This paper develops a two-stage investment-and-bargaining model of marital behavior under circumstance-contingent bride-price repayment in China. In Stage 1, spouses simultaneously choose relationship-specific investments in a non-cooperative game. In Stage 2, after investments and the legally relevant state are realized, they divide marital surplus according to a generalized Nash bargaining solution with divorce as the fixed disagreement outcome. Under the benchmark legal-state mapping, the legal rule shifts the wife’s investment incentives directly because observable consequences of her investment can affect anticipated repayment and hence her future disagreement payoff; the husband’s own investment condition contains no analogous direct legal-return term. Under a quadratic-linear specification, the best-response slopes have the sign of the technological interaction parameter, so technological complementarity generates strategic complementarity and technological substitutability generates strategic substitutability. A larger bride price, as a partial effect holding the anticipated repayment schedule fixed, or a steeper circumstance-contingent schedule shifts the wife’s best response outward. The husband’s equilibrium investment then rises under strategic complementarity and falls under strategic substitutability. Within the maintained agreement, affine-branch, positive-determinant, and strict-interiority regime, the quadratic-linear model has a unique Stage-1 Nash equilibrium, and the legal return can reduce, eliminate, or reverse the wife’s direct marginal hold-up wedge. The analysis illustrates how a legal rule affecting a future disagreement payoff can reshape pre-bargaining strategies.

We develop a two-stage game with vertically differentiated products and endogenous environmental quality to study unilateral carbon pricing and the Carbon Border Adjustment Mechanism (CBAM). A home EU firm and a foreign exporter choose environmental quality, then compete in prices. Under unilateral pricing, only the home firm is taxed, so the foreign exporter’s quality choice responds only indirectly through competition, not a direct tax-saving motive. CBAM corrects this by taxing imports, too. We show that this correction can defeat itself: the same charge that incentivizes upgrading also contracts the foreign firm’s margin and market share, and once the carbon price exceeds a parameter-dependent threshold, this contraction can dominate, leaving the firm choosing lower quality under CBAM than under unilateral pricing. We analytically show that, sufficiently close to free trade, the foreign firm’s equilibrium quality is higher under CBAM than under unilateral pricing, so quality backfire is a finite-carbon-price equilibrium reversal rather than a local artifact, and numerically show that the reversal occurs over a substantial part of the admissible parameter region and survives several robustness checks. A second channel, where CBAM narrows the quality gap, could increase aggregate emissions, but the backfire is not realized in our calibration. The results provide a game-theoretic explanation of how border carbon policies shape strategic quality competition in carbon-intensive trade.

Generative artificial intelligence has driven the cost of producing convincing artifacts of expertise toward zero. Signaling theory predicts that signals whose informational content rests on production cost lose that content when production becomes cheap. We formalize this for markets for expert services, a class of credence goods, modeling AI as a compression of the discernible headroom between what machines produce at negligible cost and what buyers can distinguish. Below a critical headroom no separating equilibrium in artifact-based production-side signals exists—for any single-crossing cost family, with the buyers’ discernment ceiling held fixed: the market pools, the competence premium vanishes, and able providers exit. We show that an outcome-contingent signal—a warranty backed by damages D with ex-post verifiability $\phi$—sustains a fully separating equilibrium at any level of AI capability whenever $\phi D\ge v$ (strictly for $\phi D>v$), where v is the value of a solved problem, under four institutional preconditions stated explicitly and priced in turn. The expected cost of liability turns on whether the problem is solved, not on how cheaply documents are produced, and is invariant to AI capability. Provenance certification priced as a type-independent stamp cannot restore full separation; a verified commitment to produce without generative assistance can, at the pre-AI signaling cost. Two further results endogenize the contract’s institutions: liability signaling has a minimum ticket size set by the fixed costs of a civil procedure and, under insurance, the signal-effective quantity is the retained, collectible exposure.