# Quid Pro Quo Diplomacy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

Heard from White House—assuming President Z convinces trump he will investigate “get to the bottom of what happened” in 2016, we will nail down date for visit to Washington. Good luck!

—US Special Envoy to Ukraine Kurt Volker, in text message to Ukrainian Presidential Aide Andriy Yirmak, 25 July 2019 [1]

## 2. Bargaining over Symbolic Support

## 3. A Model of Concessions, Visits, and Political Survival

#### 3.1. Bargaining

#### 3.2. Visits

#### 3.3. Domestic Political Competition

#### 3.4. Signals and Beliefs

#### 3.5. Summary of the Model Setup

- A stochastic nature determines whether a salient opportunity for a favor arises, $S\in \{0,1\}$, with $Pr(S=1)=\sigma $. Under open bargaining, all players observe S; under closed bargaining, only L and F observe S;
- If $S=1$, then bargaining occurs. Depending on the bargaining protocol, either L offers concession z, which F can accept or reject, or F demands concession z which L can accept or reject;
- F sees signal A and decides whether to visit L;
- Under open bargaining, C observes all aspects of the negotiations. Under closed bargaining, C observes whether a visit occurred and, should a visit occur, C observes the concession granted with probability q;
- Domestic political competition: C either challenges or abstains. If C plays challenge, then L is removed with probability $1-\theta $.

## 4. Visit Subgame

#### 4.1. F’s Incentive to Visit

**Lemma**

**1.**

#### 4.2. Visits Deter Domestic Political Challenges

**Proposition**

**1.**

**Informative equilibrium:**Suppose the bargaining phase results in a concession of z that is known to all players. If $z\in ({z}_{n},{z}_{0})$, then F visits if and only if $A\ge a\left(z\right)$ where $a\left(z\right)$ is the implicit function that solves

**Assumption**

**1.**

**Proposition**

**2.**

**Pooling equilibria:**If the concession is small, $z\le {z}_{n}$, then F never visits and following no visit, C attempts removal if $K\le {k}_{0}$. If the concession is large, $z\ge {z}_{0}$, then F always visits and, following a visit, C attempts removal if $K\le {k}_{0}$.

**Corollary**

**1.**

**Corollary**

**2.**

**Proposition**

**3.**

**Effect of Concessions on Occurrence and Impact of Visits**: As concessions increase,

- 1.
- Visits become more likely: $\frac{dPr\left(\mathit{visit}\right)}{dz}\ge 0$;
- 2.
- The perception of L’s strength following a visit decreases: $\frac{dE\left[\theta \right|\mathit{visit}]}{dz}\le 0$;
- 3.
- The perception of L’s strength following no visit decreases: $\frac{dE\left[\theta \right|\mathit{non-}\mathit{visit}]}{dz}\le 0$.These inequalities are strict if $z\in ({z}_{n},{z}_{0})$.

## 5. Open Bargaining

**Proposition**

**4.**

**Proposition**

**5.**

## 6. Closed Bargaining

#### 6.1. F as Proposer

**Proposition**

**6.**

#### 6.2. L as a Proposer

**Proposition**

**7.**

**Corollary**

**3.**

**Corollary**

**4.**

## 7. The Price of the Quid Pro Quo

**Transparency vs. Opacity**When C is fully aware of salient opportunities and the details of negotiations (as in our “open door” bargaining protocol), then an exchange of concessions for visits is never in the recipient leader’s interest. Quid pro quo diplomacy requires that bargaining occurs behind closed doors. However, our analysis reveals a more nuanced effect of transparency in diplomacy: while the domestic leader benefits from opacity in negotiations, they prefer transparency in the actual delivery of the negotiated concession. When neither the negotiations nor the concessions themselves are observed by the domestic challenger, the size of the concession increases and visits become more frequent but less informative.

**Bargaining power:**If L makes the proposal, they offer a moderate concession. Their moderate concession balances a desire to increase the likelihood of a visit while maintaining its deterrent value. As bargaining power shifts from L to F, bargaining outcomes shift to favoring F over L. The size of concessions increases, visits become more frequent, and the visits that occur have a decreased impact on L’s survival.

**Expected Salience:**When F is likely to want a favor, L suffers from a diplomatic resource curse. Because C anticipates that L has something of value to offer F, the fact that F does not make a visit in order to obtain the concession sends a strong negative signal of L’s strength. To avoid this signal of weakness, L pays more for a visit and visits become more likely and less effective. In contrast, when it is seen as unlikely that F wants a favor, the absence of a visit is less politically detrimental to L; this drives the price of the visit down, which in turn implies that any visits that do occur provide an especially powerful signal of L’s strength.

**’s cost:**As F’s costs of visiting increase, so does the price needed to offset those costs. There are three distinct costs that F must factor into their visit decisions: the material and opportunity costs of travel, $\tau $; the reputational cost of associating with a soon-deposed leader, $\rho $; and the risk that any agreed-upon deal does not become implemented, $1-r$. A stop on a regional tour or a pull-aside at a multilateral summit can be purchased more cheaply than a trip undertaken solely for the bilateral visit. Dictators and human rights abusers will likely see a steeper price for their diplomatic engagements. A policy concession requiring long-term implementation will need to be greater than its cash equivalent, as the policy concession carries the risk that L fails to survive in office long enough to implement it.

**Ex-ante survival prospects:**Prior expectations of the likelihood that L will survive affect the size of concessions and the likelihood of visits. Intuitively, ex-ante survival prospects affect both the supply and demand of visits. If L is likely to be deposed, then F needs larger concessions to compensate for the risk they assume due to the potential reputational cost as well as the possibility that the concession does not become implemented. When pessimistic about her survival prospects, L values visits highly and is willing to make larger concessions. Thus, when L’s regime is perceived to be unstable, the supply of visits is low and the demand for them is high, so the price is driven upwards. Figure 3 illustrates the impact of survival prospects on concessions when L has proposal power and officeholding incentives are dominant ($\Psi \to \infty $).

**Quality of intelligence**The basis of the quid pro quo is that F has some private information about the strength of L’s regime. The number of trials, n, may be interpreted as the quality of F’s intelligence. Both leaders’ payoffs are increasing in n: the visit’s deterrent value is increasing in the precision of the information that guided F’s decision to conduct the visit, enhancing L’s survival prospects, and in turn, L is willing to pay more for the visit, improving F’s payoff. F’s improved intelligence also means that F can better avoid visits with leaders that will be soon be removed and avoid the costs associated with such a diplomatic misstep. An empirical implication is that visits with a US president—whose decisions are informed by USD 80 billion worth of annual intelligence gathering [29]—are far more valuable to recipient leaders than visits are with, for example, a Canadian Prime Minister, who has no formal intelligence apparatus of his own [30]. This relative valuation is not a function of the the countries’ relative prestige or influence but rather of the quality of private information that their leaders have access to. If we suppose that leaders face similar travel and opportunity costs for foreign visits (similar $\tau $ and $\rho $), then US presidents should travel more than Canadian leaders because they can extract larger concessions in return.

## 8. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Bayesian Updating

#### Appendix A.2. Timing of Signals

#### Appendix A.3. Open vs. Closed Bargaining and Intermediate Transparency

#### Appendix A.4. Decision to Visit

**Proof**

**of**

**Lemma**

**1.**

**Proof**

**of**

**Propositions**

**1**

**and**

**2.**

**Proof**

**of**

**Corollary**

**2.**

**Proof**

**of**

**Proposition**

**3.**

#### Appendix A.5. Open/Transparent Bargaining

**Proof**

**of**

**Proposition**

**4.**

## Appendix B. Bargaining behind Closed Doors

**Proof**

**of**

**Proposition**

**6.**

**Proposition**

**A1.**

**Proof**

**of**

**Proposition**

**A1.**

#### L as a Proposer

**Proof**

**of**

**Proposition**

**7.**

**Proof**

**of**

**Corollary**

**4.**

## Notes

1 | Quote from an interview conducted by [19]. |

2 | https://history.state.gov/historicaldocuments/frus1964-68v29p1/d354 (accessed on 1 April 2024). |

3 | https://history.state.gov/historicaldocuments/frus1955-57v14/d175 (accessed on 1 April 2024). |

4 | Ref. [6], in contrast, considers how public diplomacy can be used for foreign antagonism rather than support. |

5 | While the “open” versus “closed” distinction bundles together multiple features of the bargaining structure, any intermediate cases are effectively nested within the two extreme cases. See Appendix A.3 of the Appendix A. |

6 | The model considers $A\in [0,n]$. The standard binominal setup considers only integers. While ${\sum}_{x=0}^{n}p\left(x\right)=1$, the integral ${\int}_{0}^{n}p\left(x\right)\ne 1$. Hence throughout we need to standardize by $P\left(n\right)$. |

7 | The results in Proposition 6 hold for $\sigma \to 1$. However, if C is completely certain, $\sigma =1$, then F can shake down L to an even greater extent. We characterize this pathological case in the Appendix A (Proposition A1). |

8 | The figure was constructed assuming $n=10$, $\Psi \to \infty $ (and L’s payoff rescaled for the graph), $r=1$, $\rho =2$ and $\tau =0.1$. |

9 | The figure is constructed using $n=10$, $q=1$ and $\alpha +\beta =6$. |

## References

- Savage, C.; Williams, J. Read the Text Messages between U.S. and Ukrainian Officials. The New York Times, 2019. Available online: https://www.nytimes.com/interactive/2019/10/04/us/politics/ukraine-text-messages-volker.html (accessed on 1 April 2024).
- Permanent Select Committee on Intelligence. Transcript: Kent and Taylor Public Testimony in Front of House Intelligence Committee Washington Post, 2019. Available online: https://www.washingtonpost.com/politics/2019/11/14/transcript-kent-taylor-public-testimony-front-house-intelligence-committee/ (accessed on 1 April 2024).
- McManus, R.W. Making it personal: The role of leader-specific signals in extended deterrence. J. Polit.
**2018**, 80, 982–995. [Google Scholar] [CrossRef] - Malis, M.; Smith, A. State Visits and Leader Survival. Am. J. Polit. Sci.
**2021**, 65, 241–256. [Google Scholar] [CrossRef] - Malis, M.; Smith, A. A global game of diplomacy. J. Theor. Polit.
**2019**, 31, 480–506. [Google Scholar] [CrossRef] - Matush, K. Harnessing Backlash: How leaders can benefit from antagonizing foreign actors? Br. J. Political Sci.
**2023**, 53, 902–918. [Google Scholar] [CrossRef] - Goldsmith, B.E.; Horiuchi, Y.; Matush, K. Does public diplomacy sway foreign public opinion? Identifying the effect of high-level visits. Am. Polit. Sci. Rev.
**2021**, 115, 1342–1357. [Google Scholar] [CrossRef] - Ostrander, I.; Rider, T.J. Presidents Abroad: The Politics of Personal Diplomacy. Polit. Res. Q.
**2019**, 72, 835–848. [Google Scholar] [CrossRef] - Lebovic, J.H.; Saunders, E.N. The diplomatic core: The determinants of high-level us diplomatic visits, 1946–2010. Int. Stud. Q.
**2016**, 60, 107–123. [Google Scholar] [CrossRef] - Nitsch, V. State visits and international trade. World Econ.
**2007**, 30, 1797–1816. [Google Scholar] [CrossRef] - Groseclose, T.; McCarty, N. The politics of blame: Bargaining before an audience. Am. J. Polit. Sci.
**2001**, 45, 100–119. [Google Scholar] [CrossRef] - Stasavage, D. Open-door or closed-door? Transparency in domestic and international bargaining. Int. Organ.
**2004**, 58, 667–703. [Google Scholar] [CrossRef] - Perlroth, A. Posturing in Bargaining to Influence Outsiders. In Working Paper, 2019; Stanford University: Stanford, CA, USA, 2019; Available online: https://www.gsb.stanford.edu/sites/gsb/files/phd-job-market-paper/draft-nov24_0.pdf (accessed on 1 April 2024).
- Andersen, T.B.; Harr, T.; Tarp, F. On US politics and IMF lending. Eur. Econ. Rev.
**2006**, 50, 1843–1862. [Google Scholar] [CrossRef] - Vreeland, J.R.; Dreher, A. The Political Economy of the United Nations Security Council: Money and Influence; Cambridge University Press: Cambridge, UK, 2014. [Google Scholar]
- Fang, S. The informational role of international institutions and domestic politics. Am. J. Polit. Sci.
**2008**, 52, 304–321. [Google Scholar] [CrossRef] - Shadmehr, M.; Boleslavsky, R. International pressure, state repression, and the spread of protest. J. Polit.
**2022**, 84, 148–165. [Google Scholar] [CrossRef] - Huseynov, E. Freeze the Dictator Out. Foreign Policy. 2016. Available online: https://foreignpolicy.com/2016/03/30/freeze-the-dictator-out-azerbaijan-aliyev-obama-nuclear-security-summit/ (accessed on 1 April 2024).
- Myrick, R.; Weinstein, J. Making Sense of Human Rights Diplomacy: Evidence from a US campaign to free political prisoners. Int. Organ.
**2022**, 76, 379–413. [Google Scholar] [CrossRef] - Office of the Vice President. Readout of Vice President Biden’s Meeting with President Ilham Aliyev of Azerbaijan. 2016. Available online: https://obamawhitehouse.archives.gov/the-press-office/2016/03/31/readout-vice-president-bidens-meeting-president-ilham-aliyev-azerbaijan (accessed on 1 April 2024).
- Gogia, G. Political Graffiti behind Bogus Jailing in Azerbaijan. Human Rights Watch. 2020. Available online: https://www.hrw.org/news/2020/02/18/political-graffiti-behind-bogus-jailing-azerbaijan (accessed on 1 April 2024).
- O’Grady, S. Meet Ali Bongo Ondimba, Obama’s Man in Africa. Foreign Policy, 2016. Available online: http://foreignpolicy.com/2016/04/05/meet-ali-bongo-ondimba-obamas-man-in-africa/ (accessed on 1 April 2024).
- Bernstein, R. Bush Visit Will Lift Poland to Status of Special Friend. The New York Times, 2003. Available online: https://www.nytimes.com/2003/05/29/world/bush-visit-will-lift-poland-to-status-of-special-friend.html (accessed on 1 April 2024).
- Britain and Libya Unveil Energy and Arms Deals. The New York Times, 2007. Available online: https://www.nytimes.com/2007/05/30/world/africa/30iht-30libya.5922646.html (accessed on 1 April 2024).
- Gaddafi Visit Seals French Deals. BBC News, 2007. Available online: http://news.bbc.co.uk/2/hi/africa/7135788.stm (accessed on 1 April 2024).
- McAuley, J. France’s Sarkozy detained over allegations of taking money from Libya’s Gaddafi. The Washington Post, 2018. Available online: https://www.washingtonpost.com/world/frances-sarkozy-detained-over-allegations-of-bribery-by-libya/2018/03/20/a51dc6f1-7afa-421c-be87-e30801ed9e24_story.html (accessed on 1 April 2024).
- Alt, J.E.; Calvert, R.L.; Humes, B.D. Reputation and Hegemonic Stability: A Game-Theoretic Analysis. Am. Polit. Sci. Rev.
**1988**, 82, 445–466. [Google Scholar] [CrossRef] - Banks, J. Signaling Games in Political Science; Psychology Press: London, UK, 1991; Volume 46. [Google Scholar]
- DeVine, M.E. Intelligence Community Spending: Trends and Issues; Congressional Research Service: Washington, DC, USA, 2019; Volume 7, p. 5700. [Google Scholar]
- Robinson, P. The Viability of a Canadian Foreign Intelligence Service. Int. J.
**2009**, 64, 703–716. [Google Scholar] [CrossRef] - Joseph, M.; Malis, M. Covert Action and Cover Stories, 2024. Working Paper. Available online: https://mattmalis.github.io/research/ (accessed on 16 April 2024).

**Figure 1.**Probability of regime change (RC) given threshold $a\left(z\right)$ under open bargaining.

F, Foreign Power | $\mathrm{L}\mathrm{Survives}$ | $\mathrm{Regime}\mathrm{Change}$ |

Visit | $Sz-\tau $ | $S\phantom{\rule{0.166667em}{0ex}}r\phantom{\rule{0.166667em}{0ex}}z-\tau -\rho $ |

Non-visit | 0 | 0 |

L, Leader | $\mathrm{L}\mathrm{Survives}$ | $\mathrm{Regime}\mathrm{Change}$ |

Visit | $\Psi -z$ | $-z$ |

Non-visit | $\Psi $ | 0 |

C, Challenger | $\mathrm{Status}\mathrm{Quo}$ | $\mathrm{Regime}\mathrm{Change}$ |

Challenge | $-K$ | $1-K$ |

Abstain | 0 | n.a. |

K∼$U[0,1]$ | C’s cost of challenging |

$\theta \in [0,1]$ | L’s regime strength, with prior distribution $Beta(\alpha ,\beta )$ |

$A\in [0,n]$ | F’s private signal of regime strength |

$z\ge 0$ | Concession offered in exchange for a visit |

$\Psi >0$ | L’s valuation of holding office |

$S\in \{0,1\}$ | Salience of concession for F, with prior $Pr(S=1)=\sigma $ |

$r\in [0,1]$ | Probability that F retains a concession following L’s removal |

$\tau >0$ | F’s fixed/opportunity cost for visiting |

$\rho >0$ | F’s conditional/reputational cost for visiting if L is subsequently removed |

$\sigma \in (0,1)$ | Expected salience: C’s prior belief of $Pr(S=1)$ |

$q\in [0,1]$ | Concession transparency: prob. C observes z after visit under closed bargaining |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Malis, M.; Smith, A.
Quid Pro Quo Diplomacy. *Games* **2024**, *15*, 14.
https://doi.org/10.3390/g15020014

**AMA Style**

Malis M, Smith A.
Quid Pro Quo Diplomacy. *Games*. 2024; 15(2):14.
https://doi.org/10.3390/g15020014

**Chicago/Turabian Style**

Malis, Matt, and Alastair Smith.
2024. "Quid Pro Quo Diplomacy" *Games* 15, no. 2: 14.
https://doi.org/10.3390/g15020014