This year's Summer Workshop on Macroeconomics and Finance featured a poster session during which Piotr Dworczak presented the model and main results from his paper titled "An economic framework for vaccine prioritization" (co-authored with Mohammad Akbarpour, Eric Budish and Scott Duke Kominers). The workshop was co-organized by SGH Warsaw School of Economics and FAME|GRAPE. The event allowed Piotr to familiarize many interested listeners with his innovative market design take on the issue of optimal allocation of scarce resources in the presence of asymmetric information.

1. An Economic Framework for Vaccine Prioritization
Mohammad Akbarpour Eric Budish Piotr Dworczak Scott Duke Kominers
Graduate School of Business, Booth School of Business Department of Economics, Harvard Business School,
Stanford University University of Chicago Northwestern University, and FAME | GRAPE and NBER
Motivation
What should guide the allocation of scarce re-
sources in a society?
• Classical economic answer: prices
• (Some) Ethicists: access to essential goods
and services should be based on need, not
ability to pay; prices should not be used in
some contexts (Sandel, Satz, etc.)
This debate played out in the context of allocating
vaccines during the Covid-19 pandemic.
What we do
A market-design approach to socially optimal alloca-
tion of Covid-19 vaccines:
• specification of social and individual preferences
over vaccination;
• strategic environment with agents
– having private information,
– making endogenous choices about what
actions to take absent receiving a vaccine;
• incorporating ethical and equity concerns, as
well as externalities;
• endowing the designer with an arbitrary infor-
mation structure, but also
• allowing the designer to use prices to screen for
unobservable characteristics.
Key insight: Dichotomy between prices versus pri-
orities is artificial; the optimal mechanism combines
prices and priorites.
Model #1
• Designer controls the allocation of vaccines (that become
available gradually over time) to a unit mass of agents.
• Prior to receiving a vaccine, each agent takes a binary
decision a ∈ {Safe, Risky}.
• Each agent is characterized by five parameters:
– v: the private socio-economic benefit of
choosing a = Risky relative to a = Safe, not
including Covid-related risk;
– h: the private health benefit of choosing
a = Safe relative to a = Risky;
– vex: the socio-economic externality gener-
ated by the agent choosing a = Risky relative
to a = Safe, not including Covid-related risk;
– hex: the health externality generated by the
agent choosing a = Safe relative to a = Risky;
– λ: a social welfare weight.
Model #3
• Each agent observes (at least) their private
benefits v and h.
• Designer does not directly observe which
action was taken, and does not observe any
of the agents’ characteristics (including the
welfare weights).
• Designer does observe one of finitely many
labels i ∈ I for each agent, and knows the
distribution of characteristics.
Most important equation:
Vi(r) = Λi(r)
1 − Gi(r)
gi(r)
| {z }
weighted utility
+ α
r −
1 − Gi(r)
gi(r)
| {z }
revenue
+ E [Tex|i, r]
| {z }
externality
.
Model #4
• Tex is the externality generated by vaccinat-
ing the agent; if v and h are independent of
vex and hex conditional on i:
E[Tex|i, r] = vi
ex · P(a = Safe|i, r)]+
+hi
ex · P(a = Risky|i, r),
where vi
ex = E[vex|i] and hi
ex = E[hex|i].
• Λi(r) is the expected welfare weight:
Λi(τ) = E[λ|i, r ≥ τ].
Model #2
• Payoff of agent vaccinated at time t, enjoying
the benefits of vaccination for a fraction δ(t) of
the duration of the pandemic:
δ(t) [v + h]
| {z }
post-vacc.
+(1 − δ(t)) [max{v, h}]
| {z }
pre-vacc.
− p
• Willingness to pay (WTP) is r = min{v, h}.
• Designer’s payoff (where α ≥ 0):
1Safe(λ(δ(t)v − p) + δ(t)vex)+
+1Risky(λ(δ(t)h − p) + δ(t)hex) + αp.
Derivation of Optimal Mechanism Illustrative Example
Fig.1. Across-group allocation. Fig.2. An example of optimal mechanism when prices can (right panel) or cannot (left panel) be used with three groups
Results
Result 1
Suppose prices cannot be used (random al-
location within each group). It is optimal to
vaccinate groups sequentially according to
V i = E[Vi(r)| i].
Result 2
It is optimal to use (within group i)
• market allocation, when Vi(r) is ↗
• free allocation, when Vi(r) is ↘
Results cnd.
Result 3
Suppose that A(0) ≥ µi (mass of agents in
group i). Then, it is optimal for all agents
in group i to receive a vaccine immediately
and for free if
min
x
E[Vi(r)| r ≤ x] ≥ max
j̸=i, x
E[Vj(r)| r ≥ x].
Results cnd.2
Result 4
Suppose that it is optimal to use a market al-
location within group j and a free allocation
within group i. If Vj(r̄j) V i Vj(rj), then
it is optimal to start vaccinating agents in group
i first, then to vaccinate all agents in group j,
and then to vaccinate the remaining agents in
group i.
Acknowledgements
The authors thank Susan Athey, Péter Biró, Ezekiel Emanuel, Simon Finster, Navid Ghaffarzadegan, Romans Pancs, Parag Pathak,
Canice Prendergast, Hazhir Rahmandad, Tayfun Sönmez, Alex Tabarrok, Nikhil Vellodi, and numerous seminar and conference audiences
for insightful conversations and comments, as well as Joanna Krysta and Xiaoyun Qiu for excellent research assistance.