# In contrast to these two

In EHop-016 to these two themes in the literature, our paper differs in that we focus on the impact of different payment schemes used in the event of bank runs on the existence of bank run equilibria. The existing literature emphasizes a sequential service payment scheme. We focus on two other payment schemes – capped-deposit and all-or-nothing.

An outline for the paper is as follows. Section 2 presents the model. Section 3 considers competitive and socially optimal equilibria in the extended Diamond and Dybvig economy. Sections 4, 5 and 6 consider equilibrium with demand deposits, demand deposits with capped deposit guarantees, and demand deposits with all or nothing guarantees, respectively. Section 7 constructs numerical examples. Section 8 concludes. All proofs are contained in the Appendix.

2. The model

The model structure follows Diamond and Dybvig (1983). There are three time periods T ∈ 0, 1, 2 and a continuum of agents i ∈ [0, 1] each endowed with fractional holdings w(i) ??>0w(i) ??>0 of a single homogeneous good, which we call cash . These holdings cannot be further subdivided, and must be consumed or invested as a whole. Without much loss of generality, we assume cytology w(i)w(i) is Lebesgue measurable, nondecreasing in i , and Lebesgue integrable with ∫01w(i)di=1. This structure just imposes a convenient ordering and normalization of the agents’ wealth distribution function w(i)w(i) so that ∫0xw(i)di represents the wealth for agents i ∈ [0, x].