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\title[Commitment Problems] % (optional, use only with long paper titles)
{Commitment Problems}


\author{}
% Ethan Bueno de Mesquita\\ \small{Harris School of Public Policy Studies}\\ \small{University of Chicago}}




\date[]% (optional, should be abbreviation of conference name)

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 \begin{frame}<beamer>{Outline}
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\begin{document}


\begin{frame}
  \titlepage
\end{frame}

\begin{frame}{A Social Dilemma}
You would take a good action if I would credibly promise to do something in the future \pause

\

 You can't trust me to follow through on my promise 

\

 You take a different action as a result of the lack of trust that makes both of us worse off
\

The ability to commit can create a Pareto improvement

\end{frame}

\section{Costly Conflict}

\begin{frame}{Why is there Conflict?}
2 parties are having a dispute
\begin{itemize}
\item War
\item Law Suit
\item Strikes
\item Bargaining over an externality  
\end{itemize}

\ 

Conflict/Bargaining failure is costly


\

 Bargain exists making both better off 
\begin{itemize}
\item Propose: expected outcome of conflict
\end{itemize}

\

 Why is there costly conflict?
\end{frame}

\begin{frame}{The Puzzle}
Value of the good: \quad $B$

\

 Cost of conflict: \quad $c$

\

 Probability party 1 wins: \quad $p$ 

\

 If fight:
\begin{equation*}
U_{1} = pB-c \qquad U_{2} = (1-p)B-c
\end{equation*}

\

 Bargaining can yield the payoffs
\begin{equation*}
U_{1} = pB \qquad U_{2} = (1-p)B
\end{equation*}
\end{frame}


\begin{frame}{Explaining Costly Conflict}
Overconfidence

\

Indivisibility

\

Commitment Problems
\end{frame}

\begin{frame}{Negotiation and Conflict}

Divided Society with two groups:
\begin{itemize}
\item Large~($L$)
\item Small~($S$)
\end{itemize}

\

 Large divides resources, $B$
\begin{itemize}
\item Keep share $\alpha$ and give $1-\alpha$ to Small
\end{itemize}

\

 Small group can accept $1-\alpha$ or start conflict
\begin{itemize}
\item Small group wins conflict with probability $p_{2}$
\end{itemize}
\end{frame}

\begin{frame}{The Extensive Form Game}

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	\put(1.85,2.7){$\fbox{S}$}
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	%% utilities


	%% strategies
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		\put(1.85,2.7){$\fbox{S}$}
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		%% utilities


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			\put(1.85,2.7){$\fbox{S}$}
			%\put(4,2.2){$1$}

			%% utilities


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			%\put(4.6,1.5){$R'$}
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			\put(2.5,2.2){$Acq$}
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\end{frame}

\begin{frame}{Small's best-response}

No Conflict if:
\begin{equation*}
\alpha < 1-p_{2} + \frac{c}{B}
\end{equation*}
\pause

\

Conflict if:
\begin{equation*}
\alpha > 1-p_{2} + \frac{c}{B}
\end{equation*}

\

\pause
Indifferent if:
\begin{equation*}
\alpha = 1-p_{2} + \frac{c}{B}
\end{equation*}
\end{frame}

\begin{frame}{Large's best response}

 Suppose Small chooses no conflict when indifferent 

\

 Large wants to maximize her share
\begin{itemize}
\item Choose largest $\alpha \leq 1-p_{2} + \frac{c}{B}$
\end{itemize}

\

 Subgame Perfect Nash equilibrium:
\begin{itemize}
\item $\alpha^{*} = 1-p_{2} + \frac{c}{B}$
\its Conflict if $\alpha > 1-p_{2} + \frac{c}{B}$; No if $\alpha \leq 1-p_{2} + \frac{c}{B}$
\end{itemize}
\end{frame}

\begin{frame}{Preemptive Conflict}
Same model but with an initial stage in which Small can start preemptive conflict

\

 Small wins preemptive conflict with probability $p_{1} > p_{2}$

\

Idea is that Large is consolidating power
\end{frame}

\begin{frame}{Preemptive Extensive Form Game}

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	%\put(4.6,1.5){$R'$}
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	\put(2.5,2.2){$Acq$}
	\put(1.9,3.5){$\alpha$}

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		\put(2.4,1.1){\shortstack{ $u_L = \alpha B$ \\ $u_S = (1-\alpha)B$}}



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		\put(2.5,2.2){$Acq$}
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			\put(1.85,2.7){$\fbox{S}$}
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			\put(3.2,3.7){\shortstack{ $u_L = (1-p_{1})B -c$ \\ $u_S = p_{1}B-c$}}


			%% strategies
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			%\put(4.6,1.5){$R'$}
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			\end{picture}
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\begin{frame}{Preemptive Attack}
 Without preemptive conflict, Small's payoff is $p_{2}B-c$ 

\

 With preemptive conflict, Small gets $p_{1}B-c$ 

\

 Preemptive conflict is a best-response
\end{frame}

\begin{frame}{A Pareto Improvement}

Suppose large could commit to proposing $\alpha = 1-p_{1}$ 

\

 Small would accept
\begin{equation*}
p_{1}B  > p_{2}B - c
\end{equation*}

\pause

\ 

Large's Payoff
\begin{itemize}
\item Equilibrium: $(1-p_{1})B -c$
\its Suggested offer: $(1-p_{1})B$
\end{itemize}

\

Small's Payoff
\begin{itemize}
\item Equilibrium: $p_{1}B -c$
\its Suggested offer: $p_{1}B$
\end{itemize}
\end{frame}

\begin{frame}{Commitment Problem}
Large cannot commit to $\alpha = 1-p_{1}$

\

 Once Small foregoes preemptive attack, Large will renege and propose $\alpha = 1-p_{2} + \frac{c}{B} > 1-p_1$

\

 Small's payoff is then $p_{2} B -c$


\

Thus, Small launches a preemptive attack
\end{frame}

\begin{frame}{Examples}
Elites inside firm or organization blocking technological change

\

Immigration reform

\

Labor/Management dispute

\

 Negotiating with terrorists
\end{frame}


\section{Hold up}

\begin{frame}{The Hold-up Problem}
Need up-front investment by an upstream producer 

\

 After investment has taken place, bargaining power shifts to the downstream producer 

\

 Leaders to under-investment of the upstream firm 
\end{frame}

\begin{frame}{A Model}
Upstream producer produces $e$ units at cost $\frac{c}{2} \cdot e^{2}$ 

\

Downstream producer offers a price $p$ per unit
\begin{itemize}
\item Values produce at $\alpha$ per unit
\end{itemize}

\

 Upstream producer can accept the offered price or use the product by itself
\begin{itemize}
\item Values the product at $\beta < \alpha$ per unit
\end{itemize}
\end{frame}

\begin{frame}{Subgame Perfect Nash equilibrium}
 Upstream will accept any price, $p \geq \beta$ 

\

 Downstream will offer $p = \beta$ 

\

 Upstream effort will solve
\begin{equation*}
\underset{e}{\max} \; \beta e - \frac{c}{2}e^{2}
\end{equation*}

\


Optimal choice of effort: $e^{*} = \frac{\beta}{c}$
\end{frame}

\begin{frame}{Utilitarian Optimum}
 Utilitarian Planner solves:
\begin{equation*}
\underset{e}{\max} \; \alpha e - \frac{c}{2}e^{2}
\end{equation*}

\

 Planner's choice of effort: $e^{*} = \frac{\alpha}{c}$

\

 Upstream firm underinvests
\end{frame}

\begin{frame}{Examples of Hold-up Problems}
 Supplier invests in infrastructure to build product to company's specifications

\

 An inventor selling an invention to user with highest valuation 

\

 Users of specialized software

\

 A partnership where one partner invests in technical expertise and the other in client relations
\end{frame}

\begin{frame}{Policy Responses to Commitment Problems}
 Complete Contracts

\

 Decrease asset specificity

\

 Multiple Suppliers

\

 Vertical Integration

\

 Instill trust
\end{frame}


\begin{frame}{Take Aways}
 Commitment problems arise in dynamic settings due to shifting circumstances and incomplete contracting

\

 Give rise to inefficient behavior due to anticipation of future circumstances

\

 One solution is to create institutions

\

 Another solution is to add improve the contracting environment

\end{frame}















\end{document}
