Professor Ryota Iijima came over to give a talk of his recent work Auctions as Experiments. Great paper. Great insights. You can find the full paper at Professor Ryota’s Google Site. Here are some notes jotted down during the talk, along with some thoughts from discussions with fellow phd students:
Setup $n$ buyers, one indivisible good, quasi-linear preferences. Values $v_i \stackrel{iid}{\sim} F_\theta$ given state $\theta \in \Theta \subseteq \mathbb{R}$, prior $q_0$. $(F_\theta)$ has MLRP in $\theta$; each $F_\theta$ has continuous, strictly positive density on a compact $I_\theta$. Information asymmetry. Buyers observe $(\theta, v_i)$. The decision-maker (DM) observes only the $n$ realized bids. Canonical interpretation: $v_i = u(\theta, \varepsilon_i)$ — $\theta$ is a common-value component, $\varepsilon_i$ idiosyncratic. Class of auctions (“standard auctions”) Sealed bids $b_i$, ranked $b^{(1)} \ge \dots \ge b^{(n)}$; highest wins. Payment functions $\psi = (\psi_\ell)_{\ell=1}^n$, increasing and symmetric in bids; $\psi_\ell = 0$ when $b^{(\ell)} = 0$. Examples: $k$-th price ($\psi_1 = b^{(k)}$, others $0$); all-pay ($\psi_\ell = b^{(\ell)}$); own-pay-$\alpha$ ($\psi_\ell = \alpha_\ell b^{(\ell)}$). Restrict to symmetric, monotone equilibria $b_\theta^\psi$. Bid CDF: $G_\theta^\psi(b) = F_\theta((b_\theta^\psi)^{-1}(b))$. All standard auctions are revenue-equivalent at each $\theta$ (private values, i.i.d.). Remak: why does the auction format matter? If buyers observed only $v_i$ (not $\theta$), all formats would be informationally equivalent — DM could invert the bidding function and back out $v_i$. Knowing $\theta$ is what creates the competition effect: at fixed $v$, the equilibrium bid $b_\theta(v)$ shifts with $\theta$ in a way that depends on $\psi$. This is the channel of differential informativeness.
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