Non-hierarchical signalling: two-stage financing game

The literature analyzing games where some players have private information about their "types" is usually based on the duality of "good" and "bad" types (GB approach), where "good" type denotes the type with better quality. In contrast, this paper analyzes a signalling game without types hierarchy. Different types have the same average qualities but different profiles of quality over time which are their private information. We apply this idea to analyze a financing-investment game where firms' insiders have private information about the firm's profit profile over time. Some firms are "performance-improving" with increasing profit profiles; others are "stagnant" with declining profit profiles. We show that equilibrium is either pooling with debt when the economy is stagnating, or separating when the economy is growing (performance-improving firms issue debt while stagnant firms issue shares). This provides new theoretical results that cannot be explained by the standard GB models and which are consistent with some financial market phenomena.